Initial strain effects in multilayer composite laminates

A boundary integral formulation for the analysis of stress fields induced in composite laminates by initial strains, such as may be due to temperature changes and moisture absorption is presented. The study is formulated on the basis of the theory of generalized orthotropic thermo-elasticity and the governing integral equations are directly deduced through the generalized reciprocity theorem. A suitable expression of the problem fundamental solutions is given for use in computations. The resulting linear system of algebraic equations is obtained by the boundary element method and stress interlaminar distributions in the boundary-layer are calculated by using a boundary only discretization. …

A discontinuous Galerkin formulation for nonlinear analysis of multilayered shells refined theories

A novel pure penalty discontinuous Galerkin method is proposed for the geometrically nonlinear analysis of multilayered composite plates and shells, modelled via high-order refined theories. The approach allows to build different two-dimensional equivalent single layer structural models, which are obtained by expressing the covariant components of the displacement field through-the-thickness via Taylor’s polynomial expansion of different order. The problem governing equations are deduced starting from the geometrically nonlinear principle of virtual displacements in a total Lagrangian formulation. They are addressed with a pure penalty discontinuous Galerkin method using Legendre polynomial…

A Rayleigh-Ritz approach for postbuckling analysis of variable angle tow composite stiffened panels

Abstract A Rayleigh-Ritz solution approach for generally restrained multilayered variable angle tow stiffened plates in postbuckling regime is presented. The plate model is based on the first order shear deformation theory and accounts for geometrical nonlinearity through the von Karman’s assumptions. Stiffened plates are modelled as assembly of plate-like elements and penalty techniques are used to join the elements in the assembled structure and to apply the kinematical boundary conditions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed to build the trial functions. A computer code was developed to implement the propose…

Dynamic analysis of damaged magnetoelectroelastic laminated structures

In the present paper a boundary element analysis of the dynamic response of damaged magnetoelectroelastic laminate structures is presented. The problem is formulated employing generalized displacements. The mass matrix is computed by the Dual Reciprocity Method. Due to the non-homogeneous nature of the laminate the multidomain boundary element technique is employed which also straightforwardly allows the modeling of interface cracks and delaminations. The multidomain boundary element technique is implemented with imperfect interlaminar interfaces and unilateral interface conditions to prevent the physical inconsistence of the overlapping between interface nodes belonging to two different pl…

Alternative boundary integral equations for fracture mechanics in 2D anisotropic bodies

An alternative dual boundary element formulation for generally anisotropic linear elastic twodimensional bodies is presented in this contribution. The formulation is based on the decomposition of the displacement field into the sum of a vector field satisfying the anisotropic Laplace equation and the gradient of the classic Airy stress function. By suitable manipulation of the integral representation of the anisotropic Laplace equation, a set of alternative integral equations is obtained, which can be used in combination with the displacement boundary integral equation for the solution of crack problems. Such boundary integral equations have the advantage of avoiding hyper-singular integral…

Artificial neural network comparison for a SHM procedure applied to composite structures.

In this paper different architectures of Artificial Neural Networks (ANNs) for structural damage detection are studied. The main objective is to create an ANN able to detect and localize damage without any prior knowledge on its characteristics so as to serve as a realtime data processor for SHM systems. Two different architectures are studied: the standard feed-forward Multi Layer Perceptron (MLP) and the Radial Basis Function (RBF) ANNs. The training data are given, in terms of a Damage Index ℑD, properly defined using the piezoelectric sensor signal output to obtain suitable information on the damage position and dimensions. The electromechanical response of the assembled structure has b…

Spherical Harmonics Expansion of Fundamental Solutions and Their Derivatives for Homogeneous Elliptic Operators

In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansion…

A micro-mechanical model for grain-boundary cavitation in polycrystalline materials

In this work, the grain-boundary cavitation in polycrystalline aggregates is investigated by means of a grain-scale model. Polycrystalline aggregates are generated using Voronoi tessellations, which have been extensively shown to retain the statistical features of real microstructures. Nucleation, thickening and sliding of cavities at grain boundaries are represented by specific cohesive laws embodying the damage parameters, whose time evolution equations are coupled to the mechanical model. The formulation is presented within the framework of a grain-boundary formulation, which only requires the discretization of the grain surfaces. Some numerical tests are presented to demonstrate the fea…

Piezoelectric bimorph response with imperfect bonding conditions

The effect of the finite stiffness bonding between the piezoelectric plies of bimorph devices has been investigated. A boundary integral formulation for piezoelasticity, based on a multidomain technique with imperfect interface conditions, has been developed. The imperfect interface conditions between the piezoelectric layers are described in terms of linear relations between the interface tractions, in normal and tangential directions, and the respective discontinuity in displacements. Continuity of the electric potential at the interface is also assumed and an iterative procedure is implemented to avoid interface interference. Numerical analysis has been performed on bimorph configuration…

A four-node MITC finite element for magneto-electro-elastic multilayered plates

An isoparametric four-node finite element for multilayered magneto-electro-elastic plates analysis is presented. It is based on an equivalent single-layer model, which assumes the first order shear deformation theory and quasi-static behavior for the electric and magnetic fields. First, the electro-magnetic state of the plate is determined in terms of the mechanical primary variables, namely the generalized displacements, by solving the strong form of the magneto-electric governing equations coupled with the electro-magnetic interface continuity conditions and the external boundary conditions. In turn, this result is used into the layers constitutive law to infer the equivalent single-layer…

Slotted Blades Savonius Wind Turbine Analysis by CFD

In this paper a new bucket configuration for a Savonius wind generator is proposed. Numerical analyses are performed to estimate the performances of the proposed configuration by means of the commercial code COMSOL Multiphysics® with respect to Savonius wind turbine with overlap only. Parametric analyses are performed, for a fixed overlap ratio, by varying the slot position; the results show that for slot positioned near the blade root, the Savonius rotor improves performances at low tip speed ratio, evidencing a better starting torque. This circumstance is confirmed by static analyses performed on the slotted blades in order to investigate the starting characteristic of the proposed Savoni…

A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates

Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…

Post-buckling analysis of cracked multilayered composite plates by pb-2 Rayleigh–Ritz method

Abstract A pb-2 Rayleigh–Ritz variational approach for the analysis of post-buckling behavior of cracked composite plates is presented. The plate is modeled by the first order shear deformation theory taking geometric nonlinearities into account through the von Karman’s theory. General stacking sequences are considered. Cracks are modeled by using subdomain decomposition of the plate coupled with penalty techniques, used to augment the variational statement with the needed continuity conditions along the connected subdomains edges. Numerical procedures have been developed and used to validate the present solution by comparison with available literature results. Original results are then pre…

A microstructural model for homogenisation and cracking of piezoelectric polycrystals

Abstract An original three-dimensional generalised micro-electro-mechanical model for computational homogenisation and analysis of degradation and micro-cracking of piezoelectric polycrystalline materials is proposed in this study. The model is developed starting from a generalised electro-mechanical boundary integral representation of the micro-structural problem for the individual bulk grains and a generalised cohesive formulation is employed for studying intergranular micro-damage initiation and evolution into intergranular micro-cracks. To capture the electro-mechanical coupling at the evolving damaging intergranular interfaces, standard mechanical cohesive laws are enriched with suitab…

A SYMMETRIC AND POSITIVE DEFINITE BEM FOR 2-D FORCED VIBRATIONS

A BEM formulation for 2D elastodynamics in the time domain has been presented. The formulation gives a resolving system that involves boundary displacements only. The stiffness and mass matrices of the boundary discretized body are frequency independent, symmetric and positive definite

BEM analysis of a piezoelectric structural health monitoring system for delamination detection

In the present work a piezoelectric based structural health monitoring (SHM) system is analyzed with the aim of assessing the ability of the piezoelectric patch to detect both edge and embedded delaminations proper of flange-skin composite laminated structures. he boundary element model is developed for piezoelectric solids and is implemented by taking advantage of the multidomain technique to model laminated and cracked configurations. A non-linear spring model interface is then implemented in conjunction with an iterative procedure allowing for the simulation of the finite stiffness of the bonding layers as well as of the non-penetration condition of the delamination surfaces. he dynamic …

A unified formulation for multilayered smart plate advanced models

Magneto-electro-elastic (MEE) composite materials are attracting increasing consideration as they couple mechanical, electrical and magnetic fields and this makes them particularly suitable for smart applications. They are often employed as multilayered configurations that appear to be more effective than bulk MEE composites. Thus, reliable and efficient modelling tools are required for an effective design. The present talk deals with a unified formulation to derive advanced models for multilayered MEE plates. The approach is based on the condensation of the electro-magnetic state into the plate kinematics. This leads to models involving kinematical variables only, which takes the multifiel…

A boundary element formulation for magneto-electro-elastic laminates

Virtual element method for computational homogenization of composite and heterogeneous materials

Abstract In this study, a two-dimensional multi-region framework, based on the use of the Virtual Element Method (VEM), is developed for computational materials homogenization and applied to different classes of widely employed heterogeneous materials. The VEM has recently emerged as a powerful generalisation of the Finite Element Method capable of dealing with very general polygonal mesh elements, including non-convex or highly distorted elements. Such features are appealing for the treatment of problems whose analysis domains present complex or statistical morphological features, which would generally require careful and time-consuming mesh/data preparation and regularization. In this wor…

Displacement boundary method for vibrations of piezoelectric materials

Refined equivalent single layer formulations and finite elements for smart laminates free vibrations

A family of 2D refined equivalent single layer models for multilayered and functionally graded smart magneto-electro-elastic plates is presented. They are based on variable kinematics and quasi-static behavior for the electromagnetic fields. First, the electromagnetic state of the plate is determined by solving the strong form of the electromagnetic governing equations coupled with the corresponding interface continuity conditions and external boundary conditions. The electromagnetic state is then condensed into the plate kinematics, whose governing equations can be written using the generalized principle of virtual displacements. The procedure identifies an effective elastic plate kinemati…

On the effect of the adhesive on piezoelectric bimorph response

Virtual Element Method: Micro-Mechanics Applications

In this contribution we present an application of the lowest order Virtual Element Method (VEM) to the problem of material computational homogenization. Material homogenization allows retrieving material properties through suitable volume averaging procedures, starting from a detailed representation of the micro-constituents of the considered material. The representation of such microstructure constitutes a remarkable effort in terms of data/mesh preparation, especially when there is not evident microstructural regularity. For such a reason, computational micromechanics may represent a challenging benchmark for showing the potential of VEM. In this contribution, polycrystalline materials ar…

Numerical Analysis of Piezoelectric Active Repair in the Presence of Frictional Contact Conditions

The increasing development of smart materials, such as piezoelectric and shape memory alloys, has opened new opportunities for improving repair techniques. Particularly, active repairs, based on the converse piezoelectric effect, can increase the life of a structure by reducing the crack opening. A deep characterization of the electromechanical behavior of delaminated composite structures, actively repaired by piezoelectric patches, can be achieved by considering the adhesive layer between the host structure and the repair and by taking into account the frictional contact between the crack surfaces. In this paper, Boundary Element (BE) analyses performed on delaminated composite structures …

Systematic comparison of Artificial Neural Networks for a SHM procedure applied to Composite Structure

The problems related to damage detection represents a primary concern, particularly in the framework of composite structure. In fact, for this kind of structures barely visible damage can occur. Moreover, one of the major in-service damage of composite aircraft strcutures is represented by disbonds between the stiffeners and the skin undergoing dynamic or post-buckling loads. The effective implementation of a SHM system relies on the synthesis of non-destructive technique (NDT), fracture mechanics, sensors technology, data manipulation and signal processing, and it can receive a great improvement through the use of an Artificial Neural Networks. Different architectures of Artificial Neural …

On the use of the EMI for the health monitoring of bonded elements

The low weight, robustness and fatigue resistance of adhesive joints make them suitable for structural joints. A fully developed nondestructive evaluation technique however is needed to monitor and assess the quality of bonded joints. In the present paper the application of the electromechanical impedance (EMI) technique is proposed. In the EMI method a piezoelectric transducer (PZT) is attached to the structure of interest. The high sensitivity and low power consumption make the EMI method feasible for real time structural health monitoring. In this study we investigated the sensitivity of the electromechanical response of a PZT to the curing and the quality of the adhesive used for bonded…

3D boundary element analysis of delamination crack using the Modified Crack Closure Integral

Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells

Abstract An original formulation for the elastic analysis of multilayered shells is presented in this work. The key features of the formulation are: the representation of the shell mean surface via a generic system of curvilinear coordinates; the unified treatment of general shell theories via an Equivalent-Single-Layer approach based on the through-the-thickness expansion of the covariant components of the displacement field; and an Interior Penalty discontinuous Galerkin scheme for the solution of the set of governing equations. The combined use of these features enables a high-order solution of the multilayered shell problem. Several numerical tests are presented for isotropic, orthotrop…

UNA FORMULAZIONE BEM ALTERNATIVA PER LA MECCANICA DELLA FRATTURA

Sensitivity analysis of a piezoelectric SHM system for delaminated composite flange-skin structure

Magneto-Electro-Elastic Bimorph Analysis by the Boundary Element Method

The influence of the magnetic configuration on the behavior of magneto-electro-elastic bimorph beams is analyzed by using a boundary element approach. The problem is formulated by using the generalized displacements and generalized tractions. The boundary integral equation formulation is obtained by extending the reciprocity theorem to magneto-electro-elastic problems; it is numerically implemented by using the boundary element method multidomain technique to address problems involving nonhomogeneous configurations. Results under different magnetic configurations are compared highlighting the characteristic features of magnetopiezoelectric behavior particularly focusing on the link between …

Boundary element method for magneto electro elastic laminates

A boundary integral formulation and its numerical implementation are presented for the analysis of magneto electro elastic media. The problem is formulated by using a suitable set of generalized variables, namely the generalized displacements, which are comprised of mechanical displacements and electric and magnetic scalar potentials, and generalized tractions, that is mechanical tractions, electric displacement and magnetic induction. The governing boundary integral equation is obtained by generalizing the reciprocity theorem to the magneto electro elasticity. The fundamental solutions are calculated through a modified Lekhnitskii's approach, reformulated in terms of generalized magneto-el…

A hybrid virtual–boundary element formulation for heterogeneous materials

Abstract In this work, a hybrid formulation based on the conjoined use of the recently developed Virtual Element Method (VEM) and the Boundary Element Method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the Finite Element Method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary i…

A fast BEM model for 3D elastic structures with attached piezoelectric sensors

A fast boundary element model for the analysis of three-dimensional solids with cracks and adhesively bonded piezoelectric patches, used as strain sensors, is presented. The piezoelectric sensors, as well as the adhesive layer, are modeled using a 3D state space finite element approach. The piezoelectric patch model is formulated taking into account the full electro-mechanical coupling and embodying the suitable boundary conditions and it is eventually expressed in terms of the interface variables, to allow a straightforward coupling with the underlying host structure, which is modeled through a 3D dual boundary element method, for accurate analysis of cracks. The technique is computational…

High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method

Abstract A novel numerical method for the analysis of multilayered shells with cut-outs is presented. In the proposed approach, the shell geometry is represented via either analytical functions or NURBS parametrizations , while generally-shaped cut-outs are defined implicitly within the shell modelling domain via a level set function . The multilayered shell problem is addressed via the Equivalent-Single-Layer approach whereby high-order polynomial functions are employed to approximate the covariant components of the displacement field throughout the shell thickness. The shell governing equations are then derived from the Principle of Virtual Displacements of three-dimensional elasticity an…

Analysis of piezoelectric active patches performances by boundary element techniques

This paper presents the analysis of active piezoelectric patches for cracked structures by Boundary Element Method. A two dimensional boundary integral formulation based on the multidomain technique is used to model cracks and to assemble the multi-layered piezoelectric patches to the host damaged structures. The fracture mechanics behavior of the repaired structures is analyzed for both perfect and imperfect interface between patches and host beams. The imperfect interface, representing the adhesive between two different layers, is modeled by using a “Spring Model” that involves linear relationships between the interface tractions, in normal and tangential directions, and the respective di…

MULTIDOMAIN BOUNDARY ELEMENT MODEL FOR CRACKS IN MAGNETO-ELECTRO-ELASTIC MATERIALS

Boundary elements analysis of adhesively bonded piezoelectric active repair

Abstract This paper presents the analysis of active piezoelectric patches for cracked structures by the boundary element method. A two-dimensional boundary integral formulation based on the multidomain technique is used to model cracks and to assemble the multi-layered piezoelectric patches to the host damaged structures. The fracture mechanics behavior of the repaired structures is analyzed for both perfect and imperfect interface between patches and host beams. The imperfect interface, representing the adhesive between two different layers, is modeled by using a “spring model” that involves linear relationships between the interface tractions, in normal and tangential directions, and the …

Analysis of piezoelectric composite laminates with edge delamination

Composite piezoelectric laminates play a crucial role in the development of the smart structures technology for aeronautical and aerospace applications, since they combine the mechanical features of the classical laminates with the additional capability to sense deformation and to adapt the structural response accordingly, allowing in this way an efficient structural control, which is achieved by exploiting the features of the electromechanical coupling. In piezoelectric devices the electrical and mechanical loads give rise to stresses whose intensity can be sufficiently high to lead to the failure of the material, especially if damage is present. In this framework, a topic of great relevan…

Postbuckling analysis of cracked stiffned plates by pb–2 Rayleigh-Ritz method

A Rayleigh-Ritz approach for the analysis of buckling and post-buckling behavior of cracked composite stiffened plates is presented. The structure is thought as the assembly of plate elements modeled by the first order shear deformation theory. Continuity along the edges common to contiguous elements are enforced by using penalty techniques, which also allow to straightforwardly implement efficient crack modeling strategies. General symmetric and unsymmetric stacking sequences are considered and numerical procedures have been developed and used to validate the present solution by comparison with FEA results. Original results are also presented for post-buckling solution of multilayered stif…

Boundary Integral Formulation for Composite Laminates in Torsion

The three-dimensional elastic stress state in a general composite laminate under twisting load is given. The analysis is carried out through an integral equation formulation that is numerically solved by the boundary element method. The integral representation of the elastic behavior is deduced by means of the reciprocity theorem applied to the actual response of each ply and the problem's analytical singular fundamental solutions. The interface continuity conditions due to perfect bonding are considered to complete the laminate mathematical model. The method permits the analysis for generally stacked laminates having general shape of the cross section. By virtue of the formulation characte…

Discontinuous Galerkin models for composite multilayered shells with higher order kinematics

Composite multilayered shells are widely employed in aerospace, automotive and civil engineering as weight-saving structural components. In multilayered shells, despite its versatility, the interplay between the curved geometry and the properties of the composite layers induces a complex distribution of the mechanical fields, which must be accurately resolved to safely employ generally curved composite shells as load-bearing structures. The problem can be addressed through the two-dimensional shell theories, which are based on suitable assumptions on the behavior of the mechanical fields throughout the thickness of the considered structures and are a viable strategy for reducing the computa…

Post-Buckling Analysis of Damaged Multilayered Composite Stiffened Plates by Rayleigh-Ritz Method

A Rayleigh-Ritz approach for the analysis of buckling and post-buckling behavior of cracked composite stiffened plates is presented. The structure is modeled as the assembly of plate elements modeled by the first order shear deformation theory and taking geometric nonlinearities into account through the von Karman’s theory assumptions. Continuity along the plate elements connected edges and the enforcement of rigid and elastic restraints of the plate boundaries are obtained by using penalty techniques, which also allow to straightforwardly implement efficient crack modeling strategies. General symmetric and unsymmetric stacking sequences are considered and numerical procedures have been dev…

Variable kinematics models for multilòayered smart plates

Families of layer-wise and equivalent single layer advanced finite elements for the geometrically nonlinear analysis of smart multilayered plates are formulated in a unified framework. The proposed modeling strategy reduces the multifield problems to an effective mechanical plate by the condensation of the electromechanical state into the plate kinematics, which is assumed as a variable order expansion along the plate thickness. Numerical results are presented to validate the proposed modeling approach and finite elements and to investigate their features.

Layer-wise and equivalent single layer models for smart multilayered plates

Layer-wise and equivalent single layer plate models for magneto-electro-elastic multiphysics laminates are presented in a unified framework. They are based on variable kinematics and quasi-static behavior of the electromagnetic fields. The electromagnetic state of each single layer is preliminary determined by solving the corresponding governing equations coupled with the proper interface continuity and external boundary conditions. By so doing, the electromagnetic state is condensed into the plate kinematics and the layer governing equations are inferred by the principle of virtual displacements. This approach identifies effective mechanical layers, which are kinematically equivalent to th…

Bending stress fields in composite laminate beams by a boundary integral formulation

Abstract The elasticity of a composite laminate under bending loads is approached through a boundary integral formulation and solved by the boundary element method. The integral equations governing the behaviour of each layer within the laminate, are deduced using the reciprocity theorem. Exact analytical singular solutions of the generalized orthotropic elasticity, i.e. the fundamental solutions of the problem, are employed as the kernels of the integral equation. The formulation does not make any assumption as to the nature of the elastic response and it allows consideration of general section geometries and stacking sequences. The solution is obtained through the enforcement of the inter…

A non-linear Ritz method for the analysis of low velocity impact induced dynamics in variable angle tow composite laminates

Abstract Variable angle tow (VAT) laminates feature composite layers reinforced by fibres following continuous curved paths and offer a wide structural design space for the manufacturing of composite components. In this work, a formulation for the analysis of the impact-induced dynamics in VAT laminated plates is proposed, implemented and tested in this work. The method is based on the adoption of first order shear deformation kinematics and includes von Karman non-linear strains. The discrete system is obtained by employing a pb-2 Ritz series expansion into the Hamilton’s variational statement, while the impact loading is modelled through Hertzian contact law. The resulting non-linear gove…

Computational Analysis of the Active Control of Incompressible Airfoil Flutter Vibration Using a Piezoelectric V-Stack Actuator

The flutter phenomenon is a potentially destructive aeroelastic vibration studied for the design of aircraft structures as it limits the flight envelope of the aircraft. The aim of this work is to propose a heuristic design of a piezoelectric actuator-based controller for flutter vibration suppression in order to extend the allowable speed range of the structure. Based on the numerical model of a three degrees of freedom (3DOF) airfoil and taking into account the FEM model of a V-stack piezoelectric actuator, a filtered PID controller is tuned using the population decline swarm optimizer PDSO algorithm, and gain scheduling (GS) of the controller parameters is used to make the control adapti…

On the repeatability of the EMI for the monitoring of bonded joints

We study the feasibility and the repeatability of the electromechanical impedance (EMI) method for the health monitoring of lightweight bonded joints. The EMI technique exploits the coupling between the displacement field and the potential field of a piezoelectric material, by attaching or embedding a piezoelectric transducer to the structure to be monitored. The sensor is excited by an external voltage and the electrical admittance which is the ratio between the electric current and the applied voltage is measured as it depends on the mechanical coupling between the transducer and the host structure. Owing to this interaction, the admittance may represent a signature for the health of the …

Free vibrations of anisotropic panels

A meshfree approach, called Displacement Boundary Method, for the analysis of in-plane and out-of-plane free vibrations of anisotropic plates is presented. The discretization process is based on the use of a modified variational principle and the static fundamental solutions of the problem operators. The stiffness and mass matrices are frequencyindependent, symmetric and positive definite and their computation requires boundary integrations of regular kernels only. Thus, the final resolving system can be solved with classical approaches by using standard numerical procedures. Numerical results are presented to show the accuracy and effectiveness of the method.

Boundary element modeling and analysis of adhesive bonded structural joints

In this paper, a boundary element technique for modeling and analysis of adhesive bonded structural joints is presented. The formulation is developed in the framework of the anisotropic elasticity and attention is focused on the application to composite structural joints built with the splicing concept technique. To model and analyze composite bonded joints a multidomain implementation of the boundary element method has been used. It has been proven well suited and very effective for the characterization of the mechanical behavior of spliced joints, allowing the analysis of the high gradient stress and strain fields near the splice lines as well as the prediction of the overall distribution…

Dynamic analysis of magneto-electro-elastic structures by a meshless approach

Buckling and post-buckling analysis of cracked stiffened panels via an X-Ritz method

Abstract A multi-domain eXtended Ritz formulation, called X-Ritz, for the analysis of buckling and post-buckling of stiffened panels with cracks is presented. The theoretical framework is based on the First-order Shear Deformation Theory and accounts for von Karman's geometric nonlinearities. The structure is modeled as assembly of plate elements. Penalty techniques are used to fulfill the continuity condition along the edges of contiguous elements and to satisfy essential boundary conditions requirements. The use of an extended set of approximating functions allows to model through-the-thickness cracks and to capture the crack opening and tip singular fields as well as the structural behav…

Nonlocal analytical solution for multilayered composite shells

Abstract In this work, an advanced nonlocal analytical formulation for the static analysis of composite shell structures is proposed. The governing equations are derived from the Principle of Virtual Displacement (PVD) [1] and are solved by the use of the Navier solution [2]. Layer-Wise models related to linear up to fourth order variations of the unknown variables in the thickness direction are treated. The modelization of multilayered structure materials takes into account the composite material properties and the nonlocal behavior based on the work of Eringen [3]. In order to take into account the nonlocality of the material, the Eringen’s stress-gradient model is employed [4]. The novel…

A fast BEM for the analysis of damaged structures with bonded piezoelectric sensors

A fast boundary element method for the analysis of three-dimensional solids with cracks and adhesively bonded piezoelectric patches, used as strain sensors, is presented. The piezoelectric sensors, as well as the adhesive layer, are modeled using a 3D state-space finite element approach. The piezoelectric patch model is formulated taking into account the full electro-mechanical coupling and embodying the suitable boundary conditions and it is eventually expressed in terms of the interface variables, to allow a straightforward coupling with the underlying host structure, which is modeled through a 3D dual boundary element method, for accurate analysis of cracks. The technique is computationa…

An Aircraft Pilot Workload Sensing System

The workload evaluation is of great importance for human error avoidance training, particularly in the use of complex systems that requires different and concurrent activities. The excessive workload harms human performance even with adverse outcomes. In the aviation field, certain flight maneuvers, such as take-off and landing, are characterized by great attention and workload demand to the pilot. Thus, a system capable of measuring pilots’ workload levels during flight could be beneficial to increase pilots’ performance. This work aims to study the initial feasibility of a device called Cockpit Pilot Warning System that monitors the pilot workload level during flight. With this aim, an ex…

A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates

Abstract In this work, a novel high-resolution formulation for multilayered composite plates is presented. The formulations is referred to as high-resolution since it combines (i) Layer-Wise plate theories, which are based on a per-layer, high-order expansion of the primary variables throughout the plate’s thickness, providing a detailed layer-level description of the sought solution; (ii) The discontinuous Galerkin method, a numerical approach based on a discontinuous representation of the unknown fields over the mesh elements and on the introduction of boundary integral operators enforcing inter-element continuity, which allow the natural treatment of high-order mesh elements and provide …

A fast 3D BEM for anisotropic elasticity based on hierarchical matrices

In this paper a fast solver for three-dimensional anisotropic elasticity BEM problems is developed. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. The application of hierarchical matrices to the BEM solution of anisotropic elasticity problems has been numerically demonstrated highlighting both accuracy and efficiency leading to almost linear computational complexity.

On the dynamic behavior of piezoelectric active repair by the boundary element method

The dynamic behavior of piezoelectric active repair bonded on cracked structures is analyzed in this article. The boundary element code used to perform the simulations is implemented in the framework of piezoelectricity in order to model the coupling between the elastic and the electric fields, which represents the most important feature of piezoelectric media. The fracture mechanics problem, i.e. the crack, as well as the bonding layer between the host structure and the active patch is modeled by means of the multidomain technique provided with an interface spring model. More particularly, the spring interface model allows considering the bonding layer as a zero-thickness elastic ply char…

Nonlinear free vibrations of composite structures via the X-Ritz method

The analysis of large amplitude vibrations of thin-walled cracked structures build as plate assembly is considered in this study. The problem is addressed via a Ritz approach, called X-Ritz, based on the first order shear deformation theory and von K´arm´an’s geometric nonlinearity assumptions. The trial functions are expressed as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour; boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions. Results are presented, which illustrate the influence of cracks on the stiffening effect due to large amplitude vibrations.

A smart composite-piezoelectric one-dimensional finite element model for vibration damping analysis

A one-dimensional finite element method for generally layered smart beams is presented in this paper. The model implements the first-order shear deformation beam theory and is based on the preliminary analytical condensation of the electric state to the mechanical state. This allows us to establish an effective mechanical beam kinematically equivalent to the original smart beam including the effects of electro-elastic couplings. The contributions of the external electric loads are included in both the equivalent stiffness properties and the equivalent mechanical boundary conditions. Hermite shape functions, which depend on parameters representative of the staking sequence through the equiv…

A Strain Sensing Structural Health Monitoring System for Delaminated Composite Structures

Structural Health Monitoring (SHM) for composite materials is becoming a primary task due to their extended use in safety critical applications. Different methods, based on the use of piezoelectric transducers as well as of fiber optics, has been successfully proposed to detect and monitor damage in composite structural components with particular attention focused on delamination cracks.In the present paper a Structural Health Monitoring model, based on the use of piezoelectric sensors, already proposed by the authors for isotropic damaged components, is extended to delaminated composite structures. The dynamic behavior of the host damaged structure and the bonded piezoelectric sensors is m…

Piezoelectric patches for the active repair of delaminated structures

Analytical solution for the dynamic analysis of magneto-electro-elastic laminated beams

A FEM piezoelectric beam model for damping circuit analysis

A finite element, developed for straight generally layered smart beam, is used to investigate vibration damping capability of circuit elements. First, the electric state is analytically condensed to kinematical quantities and the mechanical model is then written for shear deformable Timoshenko’s beam including the effects of electro-elastic couplings stacking sequence. The contributions of the external electric loads on both the equivalent stiffness properties and the equivalent mechanical boundary conditions are also taken into account. The finite element is formulated by using Hermite shape functions, which depend on parameters representative of the staking sequence through the equivalent…

Numerical analysis of a piezoelectric structural health monitoring system for composite flange-skin delamination detection

Abstract In this paper, a piezoelectric based Structural Health Monitoring (SHM) system is proposed to detect skin/stiffener debonding and delamination cracks proper of laminated composite structures. The SHM system is analyzed by means of a boundary element code implemented in the framework of piezoelectricity. The multidomain technique, coupled with an interface spring model, is used to model laminated composite structures as well as the bonding between the host delaminated structure and the piezoelectric sensor. Static sensitivity analyses are firstly performed on a drop-ply delaminated structure in order to identify a suitable configuration for the sensor. Then, the dynamic electromecha…

Optimization design process of a morphing winglet

Aeronautic and aerospace engineering is recently moving in the direction of developing morphing wing devices, with the aim of making adaptable the aerodynamic shapes to different operational conditions. Those devices may be classified according to two different conceptual architectures: kinematic or compliant systems. Both of them embed within their body all the active components (actuators and sensors), necessary to their operations. In the first case, the geometry variation is achieved through an augmented classical mechanism, while in the second case the form modification is due to a special arrangement of the inner structure creating a distributed elastic hinges arrangement. Whatever is…

Dual Boundary Element Method for fatigue crack growth: implementation of the Richard’s criterion

A new criterion for fatigue crack growth, whose accuracy was previously tested in the literature with the Finite Element Method, is here adopted with a Dual Boundary Element formulation. The fatigue crack growth of an elliptical inclined crack, embedded in a three dimensional cylindrical bar, is analyzed. In this way in addition to the propagation angle estimated by the Sih’s criterion, it is possible to take into account a twist propagation angle. The two propagation criteria are compared in terms of shape of the propagated crack and in terms of SIFs along the crack front. The efficiency of the Dual Boundary Element Method in this study is highlighted.

An enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materials

An enhanced three-dimensional (3D) framework for computational homogenization and intergranular cracking of polycrystalline materials is presented. The framework is aimed at reducing the computational cost of polycrystalline micro simulations, with an aim towards effective multiscale modelling. The scheme is based on a recently developed Voronoi cohesive-frictional grain-boundary formulation. A regularization scheme is used to avoid excessive mesh refinements often induced by the presence of small edges and surfaces in mathematically exact 3D Voronoi morphologies. For homogenization purposes, periodic boundary conditions are enforced on non-prismatic periodic micro representative volume ele…

Free vibrations of magnetoelectric bimorph beam devices by third order shear deformation theory

A fast dual boundary element method for 3D anisotropic crack problems

In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical …

Finite elements for nonlinear free vibrations analysis of smart laminates subjected to in-plane loadings

Advanced composites, able to provide multi-functional capabilities besides the traditional structural functions, has been gaining attention in many technological fields. This inherent coupling of different physical fields can be exploited in transducer applications, structural health monitoring, vibration control, energy harvesting and other applications. Magneto-electro-elastic (MEE) composite materials are attracting increasing consideration as they couple mechanical, electrical and magnetic fields and this makes them particularly suitable for smart applications. Generally, single-phase materials exhibit either piezoelectric or piezomagnetic behavior and no direct magneto-electric couplin…

Engineering requirements for avionics of unmanned aerial system

Within the framework of the European Project WInSiC4AP, the Unmanned Aerial Vehicle (UAV) use case plays an important role in defining some of the specific constraints that on-board electronics systems must obey. Then it’s relevant to have clear view of the UAVs classification and their main characteristics especially with the focus of an Electrical UAV. Main component of the power supply are batteries, whose requirements must fulfil the tight design constraint such as lightweight, safety, pressure and temperature tolerance, cost effectiveness and cycle life. A quick look to available chemistry technology as well as market overview has been described. Regarding the power sub-system, the key…

A discontinuous Galerkin formulation for variable angle tow composite plates higher-order theories

A discontinuous Galerkin formulation for the mechanical behaviour of Variable Angle Tow multi-layered composite plates is presented. The starting point of the formulation is the strong form of the governing equations, which are obtained by means of the Principle of Virtual Displacement, the Generalized Unified Formulation and the Equivalent Single Layer assumption for the mechanical behaviour of the whole assembly. To obtain the corresponding discontinuous Galerkin formulation, an auxiliary flux variable is introduced and the governing equations are rewritten as a first-order system of partial differential equations. To link neighbouring mesh elements, suitably defined numerical fluxes are …

Ritz Solution for Transient Analysis of Variable-Stiffness Shell Structures

The dynamic response of thin-walled structures is driven by mass and stiffness distribution. As such, variable-stiffness (VS) composites offer opportunities to tune structural dynamic responses. To this extent, efficient analysis tools become increasingly important for structural analysis and design purposes. In this work, an efficient and versatile Ritz method for free vibrations and linear transient analysis of VS doubly curved shell structures is presented. VS shell structures are modeled as an assembly of shell-like domains. The shell kinematics is based on the first-order shear deformation theory, and no further assumption is made on the shallowness or on the thinness of the structure.…

On the shear influence on the free vibration behavior of magneto-electro-elastic beam

A magneto-electro-elastic Timoshenko beam model is presented and employed to study the effect of the shear strain on the free vibration behavior of the beam. Once the differential governing equation for Timoshenko magneto-electro-elastic beam is derived, the Euler-Bernoulli model is obtained by letting be zero some of the governing equation coefficients. Results for the Timoshenko and Euler- Bernoulli beam are presented in comparison with two-dimensional finite element computation.

Free vibrations analysis of cracked variable stiffness composite plates by the eXtended Ritz method

Variable stiffness composite laminates show advantageous structural features related to their enlarged design space. They are attractive candidates for advanced engineering applications where the assessment of static and dynamic behavior and strength in the presence of cracks is often required. In the present work, a single-domain extended Ritz formulation is proposed to study the free vibrations of cracked variable stiffness composite plates. The plate model is based on the first-order shear deformation theory whose primary variable, i.e. displacements and rotations, are approximated via a set of orthogonal polynomial trial functions enriched with a set of special crack functions. These fu…

Fast Hierarchical Boundary Element Method for Large Scale 3-D Elastic Problems

This chapter reviews recent developments in the strategies for the fast solution of boundary element systems of equations for large scale 3D elastic problems. Both isotropic and anisotropic materials as well as cracked and uncracked solids are considered. The focus is on the combined use the hierarchical representation of the boundary element collocation matrix and iterative solution procedures. The hierarchical representation of the collocation matrix is built starting from the generation of the cluster and block trees that take into account the nature of the considered problem, i.e. the possible presence of a crack. Low rank blocks are generated through adaptive cross approximation (ACA) …

Coupled VEM–BEM Approach for Isotropic Damage Modelling in Composite Materials

Numerical prediction of composite damage behaviour at the microscopic level is still a challenging engineering issue for the analysis and design of modern materials. In this work, we document the application of a recently developed numerical technique based on the coupling between the virtual element method (VEM) and the boundary element method (BEM) within the framework of continuum damage mechanics (CDM) to model the in-plane damage evolution characteristics of composite materials. BEM is a widely adopted and efficient numerical technique that reduces the problem dimensionality due to its underlying formulation. It substantially simplifies the pre-processing stage and decreases the compu…

Application of the 3-D boundary element method to delaminated composite structures

A three-dimensional boundary element model for anisotropic solids is presented to study the fracture mechanics behavior of delaminated composite structures. The multi-domain technique is implemented to model the layered configurations and the cracks occurring at bi-material interface. The Modified Crack Closure Integral technique is implemented to characterize the fracture mechanics behavior of delaminations in terms of the total energy release rate and mode mix phase angles. Validating analyses, performed on different delaminated configurations, have shown the effectiveness of the proposed approach. Moreover, some original results are presented to investigate the effects of the stacking se…

Nonlinear model based particle swarm optimization of PID shimmy damping control

The present study aims to investigate the shimmy stability behavior of a single wheeled nose landing gear system. The system is supposed to be equipped with an electromechanical actuator capable to control the shimmy vibrations. A Proportional-Integrative-Derivative (PID) controller, tuned by using the Particle Swarm Optimization (PSO) procedure, is here proposed to actively damp the shimmy vibration. Time-history results for some test cases are reported and commented. Stochastic analysis is last presented to assess the robustness of the control system.

Electroelastic Analysis of Piezoelectric Composite Laminates by Boundary Integral Equations

A boundary integral representation for the electroelastic state in piezoelectric composite laminates subjected to axial extension, bending, torsion, shear/bending, and electric loadings is proposed. The governing equations are presented in terms of electromechanical generalized variables by the use of a suitable matrix notation. Thus, the three-dimensional electroelasticity solution for piezoelectric composite laminates is generated from a set of two partially coupled differential equations defined on the cross section of each individual ply within the laminate. These ply equations are linked through the interface conditions, which allow restoration of the model of the laminate as a whole. …

A beam finite element for magneto-electro-elastic multilayered composite structures

Abstract A new finite element based upon an elastic equivalent single-layer model for shear deformable and straight magneto-electro-elastic generally laminated beam is presented. The element has six degrees of freedom represented by the displacement components and the cross-section rotation of its two nodes. The magneto-electric boundary conditions enter the discrete problem as work-equivalent forces and moments while the electro-magnetic state characterization constitutes a post-processing step. The element possesses the superconvergence property for the static problem of beams with uniform cross-section and homogenous material properties along the beam axis direction. Moreover, it is free…

Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions

Abstract A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficie…

A Theory for Multilayered Composite Beams

Composite laminates are nowadays widely employed as lightweight components in civil engineering, automotive and aerospace applications due to their excellent mechanical properties, such as, the high strength and stiffness per unit weight, the path loads management capability. Moreover by using composite laminated materials it is possible to manufacture large size structures with less riveted joints, which leads to a reduction of the overall structural complexity and of the manufacturing and inspection times and costs. A drawback of layered composites is represented by the the low values of throughthe-thickness tensile and shear strengths, with respect to the in-plane ones, that affect the o…

Nonlinear free vibrations analysis of cracked composite stiffened plates via X-Ritz approach

Thin and moderately thick composite multi-layered plates are widely employed in naval and aerospace structures. They can experience the presence of cracks, generated for example by corrosion, fatigue or accidental external causes, which aect their static and dynamic behaviour. As regard the dynamic characteristics of plates, many studies have focused on the linear vibration analysis of both isotropic and composite thin and thick plates, providing for a comprehensive knowledge of the plate dynamic behaviour. However, for an accurate appraisal of the plate dynamics, in some applications it is needed to investigate the nonlinear free vibration problem; a literature survey evidences that the la…

Global/local Fracture Mechanics Analyses of Advanced Aerospace Structures

Orthotropic plate dynamics by a novel meshfree method

Publisher Summary This chapter deals with a novel meshfree method for the dynamic analysis of orthotropic plates under the Kirchhoff small deflection theory. The approach starts from a modified function whose stationarity conditions lead to the meshfree plate dynamic model through a discretization process—based on the use of orthotropic plate static fundamental solutions. The resolving system obtained is characterized by—frequency independent stiffness and mass matrices, which preserve the symmetry and definiteness properties of the continuum. Moreover, these operators are computed by boundary integrals of regular kernels. The method allows the application of standard numerical routines ava…

A non-linear Ritz method for progressive failure analysis of variable angle tow composite laminates

A Ritz formulation for non-linear analysis of damage initiation and evolution in variable angle tow composite plates under progressive loading is presented. The model is built on a few key items. It assumes first order shear deformation theory kinematics and non-liner strains in the von Karman sense. The constitutive relationships are formulated in the framework of continuum damage mechanics at the ply level, so that each laminate layer can experience in-plane damage initiation and evolution, then reflected in material softening and loss of local stiffness. A Ritz polynomial expansion of the primary variables and the minimization of the total potential energy provide the discrete solution e…

Modelling stress-corrosion microcracking in polycrystalline materials by the Boundary Element Method

The boundary element method is employed in this study in conjunction with the finite element method to build a multi-physics hybrid numerical model for the computational study of stress corrosion cracking related to hydrogen diffusion in polycrystalline microstructures. More specifically a boundary integral representation is used to represent the micro-mechanics of the aggregate while an explicit finite element method is used to model inter-granular hydrogen diffusion. The inter-granular interaction between contiguous grains is represented through cohesive laws, whose physical parameters depend on the concentration of inter-granular hydrogen, diffusing along the interfaces according to the …

On the transient response of actively repaired damaged structures by the boundary element method

The transient fracture mechanics behavior of damaged structures repaired through active piezoelectric patches is presented in this paper. The analyses have been performed through a boundary element code implemented in the framework of piezoelectricity to take account of the coupling between the elastic and the electric fields, which represents the peculiar feature of piezoelectric media. The multi-domain technique has been also involved to assemble the host structures and the active patches and to model the cracks. Moreover, the patches have been considered elastically bonded to the damaged structure by means of a zero thickness adhesive layer. This has been achieved through the implementat…

A beam theory for layered composites subjected to uniformly distributed load

A theory for multilayered composite beams undergoing transverse uniformly distributed loads is presented. The formulation starts by assuming a layer-wise kinematical model characterized by third order approximation of the axial displacements and fourth order approximation of the transverse displacements. By enforcing the point-wise balance equations as well as the interface continuity conditions, the layer-wise kinematical model is rewritten in terms of a set of generalized kinematical variables associated with the beam as a whole. Stress resultants are then obtained in terms of the generalized variables derivatives and of the normal stresses applied to the top and bottom surfaces of the la…

Hierarchical-ACA DBEM for anisotropic three-dimensional time-domain fracture mechanics

Dynamic Analysis of Piezoelectric Structures by the Displacement Boundary Method

Structural Health Monitoring of delaminated composite structures by the Boundary Element method

Structural Health Monitoring (SHM) for composite materials is becoming a primary task due to their extended use in safety critical applications. Different methods, based on the use of piezoelectric transducers, strain memory alloys as well as of fibre optics, has been successfully proposed to detect and monitor damage in composite structural components with particular attention focused on delamination cracks. In the present paper a Structural Health Monitoring model based on the use of piezoelectric sensors, already proposed by the authors for isotropic damaged components, is extended to delaminated composite structures. The dynamic behavior of the host damaged structure and the bonded piez…

Advanced models for nonlocal magneto-electro-elastic multilayered plates based on Reissner mixed variational theorem

In the present work, nonlocal layer-wise models for the analysis of magneto-electro-elastic multilayered plates are formulated. An Eringen non-local continuum behaviour is assumed for the layers material; in particular, as usual in plate theories, partial in-plane nonlocality is assumed whereas local constitutive behaviour is considered in the thickness direction. The proposed plate theories are obtained via the Reissner Mixed Variational Theorem, assuming the generalized displacements and generalized out-of-plane stresses as primary variables, and expressing them as through-the-thickness expansions of suitably selected functions, considering the expansion order as a free parameter. In the …

Modal and Structural FEM Analysis of a 50 ft Pleasure Yacht

In this paper a structural Finite Element analysis of a 50 ft pleasure vessel is presented. The study is performed under different loads conditions: modal analyses have been done in order to find the natural frequencies of the vessel, structural analyses to verify the strength of the vessel to design loads. The design loads for the vessel considered are computed according to RINA rules for the construction and classification of pleasure vessels [1]. Two different composites are used for the lamination: one is a monolithic sequence of short fibre and balanced glass lamina, used for the bottom of the vessel and for structural reinforcements, the other is a sandwich made of glass fibre composi…

A boundary element model for piezoelectric dynamic strain sensing of cracked structures

A piezoelectric sensor model is here presented for the Structural Health Monitoring (SHM) of damaged structures. A boundary element approach based on the Dual Reciprocity BEM is then used to model and analyze the transient response of a piezoelectric patch bonded on a cracked beam. The BE model is written for the piezoelectric problem employing generalized displacements. The multidomain boundary element technique is implemented to model non-homogeneous and cracked configuration, taking contact conditions into account. Analyses have been carried out for an isotropic beam with a piezoelectric strip attached on it and dynamical results for the undamaged structure have been compared with FE res…

Mixed finite elements for nonlocal elastic multilayered composite plate refined theories

Abstract A novel mixed finite element formulation for the layerwise analysis of nonlocal multilayered composite plates is presented. The finite elements are formulated starting from the weak form of a set of governing equations for the laminate layers that were deduced via the Reissner Mixed Variational Theorem. The primary variables, namely displacements and out-of-plane stresses, are expressed at layer level as through-the-thickness expansions of suitable selected functions with coefficients approximated by the finite element scheme. The through-the-thickness expansion order is considered as a free parameter. This way, finite elements for different refined higher order plate theories can …

BE analysis of delaminated Composite Structures repaired with Piezoelectric Active patches

The main target of the present paper is the analysis of the fracture mechanics behavior of delaminated composite structures actively repaired through piezoelectric patches. The aim at issue has been achieved by using a boundary element code implemented to study piezoelectric solids, including, as limiting case, the applicability to linear elastic anisotropic materials. The assembled structures, made up of the damaged composite components and the piezoelectric patches, have been modelled through the multidomain technique. To take into account for the adhesive layer among the host structure and the active patch, an interface spring-model has been also implemented. The multidomain technique co…

A Grain-Scale Model of Inter-Granular Stress Corrosion Cracking in Polycrystals

In this contribution, we propose a cohesive grain-boundary model for hydrogen-assisted inter-granular stress corrosion cracking at the grain-scale in 3D polycrystalline aggregates. The inter-granular strength is degraded by the presence of hydrogen and this is accounted for by employing traction-separation laws directly depending on hydrogen concentration, whose diffusion is represented at this stage through simplified phenomenological relationships. The main feature of the model is that all the relevant mechanical fields are represented in terms of grain-boundary variables only, which couples particularly well with the employment of traction-separation laws.

Unified formulation for a family of advanced finite elements for smart multilayered plates

AbstractFamilies of layer-wise and equivalent single-layer advanced finite elements for the analysis of smart multilayered plates are formulated in a unified framework. The proposed modeling strategy reduces the multifield problem to an effective mechanical plate by the condensation of the electromechanical state into the plate kinematics, which is assumed as a variable order expansion along the plate thickness. Carrera Unified Formulation is invoked to derive the elemental stiffness and mass matrices and the mechanical and magneto-electric equivalent forces. The obtained smart plate finite element equations involves kinematical variables only and this extends the tools developed for multil…

A Microstructural Model for Micro-Cracking in Piezoceramics

Piezoelectric ceramics are employed in several applications for their capability to couple mechanical and electrical fields, which can be advantageously exploited for the implementation of smart functionalities. The electromechanical coupling, which can be employed for fast accurate micro-positioning devices, makes such materials suitable for application in micro electromechanical systems (MEMS). However, due to their brittleness, piezoceramics can develop damage leading to initiation of micro-cracks, affecting the performance of the material in general and the micro-devices in particular. For such reasons, the development of accurate and robust numerical tools is an important asset for the…

Advanced models for smart multilayered plates based on Reissner Mixed Variational Theorem

In the present work, families of equivalent singe layer and layer-wise models for the static and free vibrations analysis of magneto-electro-elastic multilayered plates are developed. The models are defined in the framework of a unified formulation, which offers a systematic approach for generating refined plate theories through suitable expansions of the through-the-thickness components of the relevant fields, considering the expansion order as a free parameter. The key features of the developed formulation are: a) the condensation of the electric and magnetic description into the mechanical representation, based on the quasi-static electric-magnetic approximation, which allows to reduce t…

An alternative BEM for Fracture Mechanics

An alternative single domain boundary element formulation and its numerical implementation are presented for the analysis of two-dimensional cracked bodies. The problem is formulated employing the classical displacement boundary integral representation and a novel integral equation based on the stress or Airy’s function. This integral equation written on the crack provides the relations needed to determine the problem solution in the framework of linear elastic fracture mechanics. Results are presented for typical problems in terms of stress intensity factors and they show the accuracy and efficiency of the approach.

Forced vibration analysis of magneto-electro-elastic beam

Boundary Element Method for Composite Laminates

The boundary element method (BEM) is a numerical technique to solve engineering/physical problems formulated in terms of boundary integral equations. Composite laminates are assemblages of stacked different materials layers, generally consisting of variously oriented fibrous composite materials

Hierarchical fast BEM for anisotropic time-harmonic 3-D elastodynamics

The paper presents a fast boundary element method for anisotropic time-harmonic 3-D elastodynamic problems. The approach uses the hierarchical matrices format and the ACA algorithm for the collocation matrix setup and a preconditioned GMRES solver for the solution. The development of this approach for the anisotropic case presents peculiar aspects which deserve investigation and are studied in the paper leading to the employed computational strategy and its effective tuning. Numerical experiments are presented to assess the method accuracy, performances and numerical complexity. The method ensures adequate accuracy allowing remarkable reductions in computation time and memory storage.

An extended Ritz formulation for buckling and post-buckling analysis of cracked multilayered plates

Abstract An extended Ritz formulation for the analysis of buckling and post-buckling behaviour of cracked composite multilayered plates is presented. The formulation is based on: (i) the First-order Shear Deformation Theory to model the mechanics of the multilayered plate; (ii) the von Karman’s theory to account for geometric non-linearities ; (iii) the use of an extended set of approximating functions able to model the presence of an embedded or edge crack and to capture the crack opening fields as well as the global behaviour within a single cracked domain. The numerical results of the buckling analyses and the equilibrium paths in the post-buckling regime are compared with the results fr…

Analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the def…

A fast dual boundary element method for 3D anisotropic crack problems

In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical …

Large deflection of magneto-electro-elastic laminated plates

Abstract A model for the large deflection analysis of magneto-electro-elastic laminated plates is derived. The first order shear deformation theory and the von Karman stress function approach are employed. A set of resolving partial differential equations involving kinematical variables and the stress function is obtained as a consequence of the preliminary condensation of the electro-magnetic state to the plate kinematics. A closed form solution for simply-supported plates is presented. Numerical results are carried out for plates consisting of piezoelectric BaTiO 3 and piezomagnetic CoFe 2 O 4 layers. These results show the influence of large deflections on the plate response and could be…

Buckling and Postbuckling of Stiffened Composite Panels with Cracks and Delaminations by Ritz Approach

A Ritz approach for the analysis of buckling and post-buckling of stiffened composite panels with through-the-thickness cracks and/or delaminations is presented. The structure is modeled as the assembly of plate elements whose behavior is described by the First-order Shear Deformation Theory and von Karman’s geometric nonlinearities. Penalty techniques ensure continuity along the edges of contiguous plate elements and the enforcement of the restraints on the external boundaries. They are also used to avoid interpenetration problems. General symmetric and unsymmetric stacking sequences are considered. A computer code has been developed and used to validate the proposed method, comparing the …

Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme

The Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well known, extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due to its underlying formulation, the BEM allows reducing the dimensionality of the proble…

Onthe repeatability of electromechanical impedance for monitoring of bonded joints

The repeatability and sensitivity of the electromechanical impedance (EMI) method when employed for the structural health monitoring of bonded joints were investigated. A simple joint was assembled by bonding an aluminum strip to a square aluminum plate. Two rounds of experiments were performed. The first set aimed at verifying the repeatability of the method. The joint was monitored by using one piezoelectric sensor. The PZT was glued to the plate and never removed, whereas a poorly bonded joint was assembled and disassembled three times. For each case, the electromechanical signature was measured during the curing of the adhesive. After the three tests, the same joint was built with a dif…

A regular variational boundary model for free vibrations of magneto-electro-elastic structures

In this paper a regular variational boundary element formulation for dynamic analysis of two-dimensional magneto-electro-elastic domains is presented. The method is based on a hybrid variational principle expressed in terms of generalized magneto-electro-elastic variables. The domain variables are approximated by using a superposition of weighted regular fundamental solutions of the static magneto-electro-elastic problem, whereas the boundary variables are expressed in terms of nodal values. The variational principle coupled with the proposed discretization scheme leads to the calculation of frequency-independent and symmetric generalized stiffness and mass matrices. The generalized stiffne…

Structural Health Monitoring of Cracked Beam by the Dual Reciprocity Boundary Element Method

In this paper a 2D boundary element model is used to characterize the transient response of a piezoelectric based structural health monitoring system for cracked beam. The BE model is written for piezoelectric non-homogeneous problem employing generalized displacements. The dual reciprocity method is used to write the mass matrix in terms of boundary parameters only. The multidomain boundary element technique is implemented to model non-homogeneous and cracked configuration, unilateral interface conditions are also considered to prevent the physical inconsistence of the overlapping between interface nodes belonging to the crack surfaces. To assess the reliability and the effectiveness of th…

An equivalent single-layer model for magnetoelectroelastic multilayered plate dynamics

Abstract An equivalent single-layer model for the dynamic analysis of magnetoelectroelastic laminated plates is presented. The electric and magnetic fields are assumed to be quasi-static and the first-order shear deformation theory is used. The formulation of the model provides for a preliminary fulfillment of the electro-magnetic governing equations, which allows to determine the electric and magnetic potential as functions of the mechanical variables. Then, by using this result, the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-elect…

Ritz Model for Damage Analysis in Variable Angle Tow Composite Plates

In this work, a Ritz method is developed for progressive damage analysis of multilayered variable angle tow (VAT) composite plates under geometrically non-linear strains. The proposed model adopts a first order shear deformation theory and considers geometric non-linearities through the von Karman assumptions. A meso-modelling approach based on Continuum Damage Mechanics is adopted for analysing the initiation and evolution of damage. The onset of damage is predicted using the Hashin’s criteria. Four damage indices are defined and computed for expressing the degradation of the mechanical properties of the material, both for fibers and matrix under either tension and compression loading. A s…

A meshfree method for transverse vibrations of anisotropic plates

A meshfree approach, called displacement boundary method, for anisotropic Kirchhoff plate dynamic analysis is presented. This method is deduced from a variational principle, which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables. The discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional. The stiffness and mass matrices obtained for the dynamic model are frequency-independent, symmetric and positive definite and their computation involves bound…

Analytical solution for composite layered beam subjected to uniformly distributed load

ABSTRACTThe article presents an analytical theory for multilayered composite beams subjected to transverse uniformly distributed loads. The formulation is based on a layerwise model characterized by third-order approximation of the axial displacements and fourth-order approximation of the transverse displacements. The layerwise kinematical model is rewritten in terms of generalized variables. The beam equilibrium equations, expressed in terms of stress resultant, allow writing the boundary value governing problem. The layerwise fields are obtained by postprocessing steps. The main advantage is to ensure the accuracy level associated to the layerwise formulations preserving the computational…

Variable kinematics models and finite elements for nonlinear analysis of multilayered smart plates

Abstract A variable kinematics approach for moderately large deflection analysis of smart magneto-electro-elastic multilayered plates is presented. The approach is based on the condensation of the electro-magnetic state into the plate kinematics, whose nonlinear strain–displacement relationships are expressed in the von Karman sense. This leads to models resulting in an effective mechanical plate, which takes the multifield coupling effects into account by the plate stiffness, inertia and loading characteristics, consistently defined as combinations of the layers material properties. By a unified approach, both equivalent single layer and layerwise models are developed formulating the assoc…

A novel boundary element formulation for anisotropic fracture mechanics

Abstract A novel boundary element formulation for two-dimensional fracture mechanics is presented in this work. The formulation is based on the derivation of a supplementary boundary integral equation to be used in combination with the classic displacement boundary integral equation to solve anisotropic fracture mechanics problems via a single-region approach. The formulation is built starting from the observation that the displacement field for an anisotropic domain can be represented as the superposition of a vector field, whose components satisfy a suitably defined anisotropic Laplace equation, and the gradient of the Airy stress function. The supplementary boundary integral equation is …

Boundary element solution for free edge stresses in composite laminates

The edge-stress problem in multilayered composite laminates under uniform axial extension is analyzed through an alternative method based on a boundary integral formulation. The basic equations of the formulation are discussed and solved by the multiregion boundary element method. Generalized orthotropic elasticity analytic fundamental solutions are employed to establish the integral equations governing the problem. The formulation is absolutely general with regard to the laminate stacking sequence and the section geometry and it does not require any aprioristic assumption on the elastic response nature. This makes the formulation suitable for an investigation of the singular behavior of th…

A Theory of Laminated Beams Subjected to Axial, Bending and Shear Load

A theory of laminated beams subjected to axial, bending and shear loads is presented in this paper. The kinematical model employed to describe the laminated beam displacement field is layer-wise in nature. Moreover it is such that the equilibrium equations and the continuity of the stress components at plies interfaces are satisfied. By using the whole set of interface continuity conditions in conjunction with the traction –free conditions on the beam top and bottom surfaces the layer-wise kinematical quantities are written in terms of the mechanical primary variables pertaining to one layer only, which are then expressed in terms of the laminated generalized displacements. The solution for…

A NEW SYMMETRIC AND POSITIVE DEFINITE BOUNDARY ELEMENT FORMULATION FOR LATERAL VIBRATIONS OF PLATES

Abstract A new symmetric and positive definite boundary element method in the time domain is presented for the dynamic analysis of thin elastic plates. The governing equations of the problem are obtained from a variational principle in which a hybrid modified functional is employed. The functional is expressed in terms of the domain and boundary basic variables in plate bending, assumed to be independent of each other. In the discretized model the boundary variables are expressed by nodal values, whereas the internal displacement field is modelled by a superposition of static fundamental solutions. The equations of motion are deduced from the functional stationarity conditions and they cons…

Microcracking in piezoelectric materials by the Boundary Element Method

A 3D boundary element model for piezoelectric polycrystalline micro-cracking is discussed in this contribution. The model is based on the boundary integral representation of the electro-mechanical behavior of individual grains and on the use of a generalized cohesive formulation for inter-granular micro-cracking. The boundary integral formulation allows to address the electro-mechanical boundary value problem in terms of generalized grain boundary and inter-granular displacements and tractions only, which implies the natural inclusion of the cohesive laws in the formulation, the simplification of the analysis pre-processing stage, and the reduction of the number of degrees of freedom of the…

Multidomain boundary integral formulation for piezoelectric materials fracture mechanics

Abstract A boundary element method and its numerical implementation for the analysis of piezoelectric materials are presented with the aim to exploit their features in linear electroelastic fracture mechanics. The problem is formulated employing generalized displacements, that is displacements and electric potential, and generalized tractions, that is tractions and electric displacement. The generalized displacements boundary integral equation is obtained by using the closed form of the piezoelasticity fundamental solutions. These are derived through a displacement based modified Lekhnitskii’s functions approach. The multidomain boundary element technique is implemented to achieve the numer…

A Microstructural Model for Micro-Cracking in Piezoceramics

Piezoelectric ceramics are employed in several applications for their capability to couple mechanical and electrical fields, which can be advantageously exploited for the implementation of smart functionalities. The electromechanical coupling, which can be employed for fast accurate micro-positioning devices, makes such materials suitable for application in micro electro-mechanical systems (MEMS). However, due to their brittleness, piezoceramics can develop damage leading to initiation of micro-cracks, affecting the performance of the material in general and the micro-devices in particular. For such reasons, the development of accurate and robust numerical tools is an important asset for th…

Interlaminar stresses in laminated composite beam-type structures under shear/bending

A boundary integral model for composite laminates under out-of-plane shear/bending is presented. The formulation proposed allows one to determine the elastic response of generally stacked composite laminates having general shape of the cross section. The integral equations governing the ply behavior within the laminate are deduced starting from the reciprocity theorem for beam-type structures. The ply integral equations are obtained by employing the analytical expression of the fundamental solution of generalized plane strain anisotropic problems. The laminate model is completed by imposing the displacement and stress continuity along the interfaces and the external boundary conditions. The…

BEM Formulation of the Trailing Edge Condition

This paper deals with a BEM formulation of the trailing edge condition to determine the potential flow field around an airfoil. It is seen the trailing edge condition is not sufficient to give an unique solution. It is necessary to assign a further condition to eliminate the nonuniqueness of the solution. The approach allows to adopt a discretization into superior order elements. Some preliminary applications show the validity of the formulation.

Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method

A novel formulation for the linear buckling analysis of multilayered shells is presented. High-order equivalent-single-layer shell theories based on the through-the-thickness expansion of the covariant components of the displacement field are employed. The novelty of the formulation regards the governing equations solution via implicit-mesh discontinuous Galerkin method. It is a high-order accurate numerical technique based on a discontinuous representation of the solution among the mesh elements and on the use of suitably defined boundary integrals to enforce the continuity of the solution at the inter-element interfaces as well as the boundary conditions. Owing to its discontinuous natur…

An implicit mesh discontinuous Galerkin formulation for higher-order plate theories

In this work, a discontinuous Galerkin formulation for higher-order plate theories is presented. The starting point of the formulation is the strong form of the governing equations, which are derived in the context of the Generalized Unified Formulation and the Equivalent Single Layer approach from the Principle of Virtual Displacements. To express the problem within the discontinuous Galerkin framework, an auxiliary flux variable is introduced and the governing equations are rewritten as a system of first-order partial differential equations, which are weakly stated over each mesh element. The link among neighboring mesh elements is then retrieved by introducing suitably defined numerical …

An analytical solution for multilayered beams subjected to ends loads

An alternative model for multilayered beams undergoing axial, shear and bending loads applied at the beam's ends is developed. It is based on a layer-wise kinematics, which inherently fulfills the equilibrium equations at layer level and the interface continuity conditions. This kinematics is suitably expressed by introducing a set of generalized variables representative of the beam midline displacement field, which become the primary variables of the problem governing equations. As a consequence, the proposed beam model exhibits the computational characteristics of an equivalent single layer model and possesses the accuracy of layer-wise beam theories, as well. Closed form solutions for di…

Analysis of FBG reflection spectra under uniform and non-uniform transverse loads

Loads applied transversely on the external surface of waveguides change their circular cross-sectional geometry generating birefringence. Due to this effect the reflected spectrum of a Fibre Bragg grating (FBG) undergoes a splitting of the single peak of the Bragg wavelength. In this work, we employed the Transfer Matrix Method (TMM) for x- and y-polarized wave-modes to model the uniform FBG reflection spectra for uniform and non-uniform transverse loads. We also performed experimental measurements for two different transverse load scenarios. The load profiles chosen for these experiments were applied on the FBG sensor through a block of steel and a roll bearing pin. Then, the modelled and …

An integrated structural health monitoring system based on electromechanical impedance and guided ultrasonic waves

We propose a structural health monitoring (SHM) paradigm based on the simultaneous use of ultrasounds and electromechanical impedance (EMI) to monitor waveguides. Methods based on the propagation of guided ultrasonic waves (GUWs) are increasingly used in all those SHM applications that benefit from built-in transduction, moderately large inspection ranges, and high sensitivity to small flaws. Meantime, impedance-based SHM promises to adequately assess locally the structural integrity of simple waveguides and complex structures such as bolted connections. As both methods utilize piezoelectric transducers bonded or embedded to the structure of interest, this paper describes a unified SHM para…

A fast hierarchical BEM for 3-D anisotropic elastodynamics

Hierarchical-ACA DBEM for Anisotropic Three-Dimensional Time-Harmonic Fracture Mechanics

A hierarchical BEM solver for the analysis of three-dimensional anisotropic time-harmonic fracture mechanics problems is presented. A thorough investigation on the relations and interactions between the numerically computed anisotropic fundamental solutions and the algorithm used to approximate the blocks of the hierarchical matrix, namely Adaptive Cross Approximation, is carried out leading to the employed computational strategy. The use of the hierarchical matrices and iterative solvers is proved as an effective technique for speeding up the solution procedure and reducing the required memory storage in time-harmonic three-dimensional anisotropic fracture mechanics problems.

Analysis of composite laminates with imperfect bonding conditions

A multidomain boundary integral formulation for the analysis of composite laminates with imperfect interlaminar interfaces is presented. An imperfect interface refers to a zero-thickness interfacial layer across which displacement discontinuity may occur while interlaminar tractions must remain continuous. The displacement discontinuity is considered through a spring model in order to model the adhesive layer among two adjacent laminae. No auxiliary elements are needed to implement the imperfect interface since the spring coefficients, characterizing the different bonding interface conditions, are taken into account inside the assembled influence matrices. To assess the reliability and the …

Multidomain BEM for crack analysis in stiffened anisotropic plates.

The present paper is concerned with the application of a boundary element model for the analysis of cracks in stiffened composite panels. The panel stiffeners are reduced to equivalent strips and the multidomain technique is used to model panel zones presenting different properties (skin and stiffeners equivalent strip). Also the crack is modeled exploiting the multidomain formulation. Evaluation of stress intensity factors is performed for representative problems.

Buckling and post-buckling analysis of cracked composite plates via a single-domain Ritz approach

Thin and moderately thick composite multi-layered plates are widely employed in many engineering applications, especially in naval and aerospace structures. These structural components can experience in service the presence of cracks, generated for example by corrosion, fatigue or accidental external causes. Cracks can affect the load carrying capability, buckling and post-buckling behaviour of plates; therefore, their effects need to be investigated and taken into account for fail safe or damage tolerant design. Additionally, attention should be devoted to the interaction of cracks with buckling and post-buckling behaviour, as the energy release rate in post-buckling regimes can be adverse…

On the Effect of Slotted Blades on Savonius Wind Generator Performances by CFD Analysis

In this paper a new bucket configuration for Savonius wind generator is proposed. With the aim to increase the effect of the overlap ratio RS on the wind turbine performances and to increase the amount of lift force able to produce torque and power, slotted blades are investigated by means of the Computational Fluid Dynamics analysis. The numerical analyses are performed by Comsol Multiphysics® and the results obtained for a Savonius wind turbine with overlap only are compared to numerical and experimental benchmarks. Parametric analyses are performed, for fixed overlap ratio, by varying the slot angle β and the results show that for low angle β the Savonius rotor exploits improved performa…

An equivalent single-layer approach for free vibrations analysis of smart laminated thick composite plates

An equivalent single-layer model for the free vibration analysis of smart laminated plates is presented. The electric and magnetic fields are assumed to be quasi-static and third-order in-plane kinematics is employed to adequately take the shear influence into account when the plate thickness increases. The model governing equations are the plate equations of motion written in terms of mechanical primary variables and effective stiffness coefficients, which take the multifield coupling effects into account. The model shows that the surfaces magneto-electric boundary conditions enter the definitions of the laminate forces and moments resultants. Moreover, it reveals that new stiffness terms,…

A framework for aeroelastic analysis employing higher-order structural and aerodynamic theories

Aeroelasticity is an essential tool for the analysis and design of structures whose operating conditions involve the interaction with aerodynamic loads, and it finds application in aerospace, mechanical and civil applications. Involving the analysis of generally complex interactions between fluids and structures, aeroelastic analyses tend to be computationally expensive, thus often resorting to suitable simplification either in the structural or aerodynamic modelling, so to reduce the computational burden. On the other hand, the employment of composite materials in several engineering sectors has given the designer an unprecedented freedom in terms of design choices. In structures subjected…

Una formulazione agli elementi di contorno per l’analisi unificata aeroacustica ed aerodinamica di un treno ad alta velocità

Boundary element method for magneto-electro-elastic laminates

A boundary integral formulation and its numerical implementation are presented for the analysis of magneto-electro-elastic media. The problem is formulated by using a suitable set of generalized variables. The governing boundary integral equation is obtained by generalizing the reciprocity theorem to the magneto-electro-elasticity. The fundamental solutions are calculated through a modified Lekhnitskii’s approach, reformulated in terms of generalized magneto-electroelastic displacements. To assess the reliability and effectiveness of the formulation, some numerical analyses have been carried out and the convergence of the method has been studied. The multidomain approach has been developed …

Boundary Element Analysis of Magneto-Electro-Eleastic Bimorph Actuators

Large deflection analysis of magneto-electro-elastic laminates

Magneto-electro-elastic (MEE) composites containing piezoelectric and piezo-magnetic phases have recently emerged for many application smart structures technology. In this framework, the development of tools to analyze the MEE laminates is essential for their efficient design. In the present work, a model for the large deflection analysis of MEE laminated plates is proposed. The first order shear deformation theory and the von Karman stress function approach are employed to model the mechanical behavior whereas quasi-static behavior is assumed for the electro-magnetic quantities. First, the magneto-electric problem is solved in terms of the plate mechanical primary variables. In turn, this …

A hierarchical-ACA technique for large-scale acoustic simulations: complex geometries with sound adsorbent materials

In this paper a boundary element approach for acoustic simulations based on the hierarchical-matrix format coupled with the adaptive cross approximation (ACA) algorithm and a hierarchical GMRES solver is presented. The cluster tree is generated using preliminary considerations of the prescribed boundary conditions. An improved ACA algorithm, applied, separately, to Neumann, Dirichlet and mixed Robin conditions, is described. Numerical results are presented to show the new approach to be up to 50% faster than conventional ACA approach.

A one-dimensional model for dynamic analysis of generally layered magneto-electro-elastic beams

Abstract A new one-dimensional model for the dynamic problem of magneto-electro-elastic generally laminated beams is presented. The electric and magnetic fields are assumed to be quasi-static and a first-order shear beam theory is used. The electro-magnetic problem is first solved in terms of the mechanical variables, then the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-electro-mechanical couplings into account. Additional terms, which involve the third spatial derivative of the transverse displacement, also occur as a result of the …

Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach

Abstract Variable Angle Tow (VAT) composite plates are characterized by in-plane variable stiffness properties, which opens to new concepts of stiffness tailoring and optimization to achieve higher structural performance for advanced lightweight structures where damage tolerance consideration are often mandatory. In this paper, a single-domain eXtended Ritz formulation is proposed to study the buckling behaviour of variable stiffness laminated cracked plates. The plate behaviour is described by the first order shear deformation theory whose generalized displacements, namely reference plane translations and rotations, are expressed via suitable admissible trial functions. These consist of a …

A PROCEDURE FOR THE EVALUATION OF INSTALLED PROPELLER NOISE

Abstract A method for the prediction of the acoustics of a propeller in the flow-field of a wing is presented. The method is used to study the noise generated by the unsteady loading induced on the propeller as it passes through the wing flow-field. Both the aerodynamic and acoustic methods are previously proven techniques, the aerodynamic method being based on a combination of free wake analysis and a three-dimensional boundary element method, while the acoustic calculation is a full-surface, moving medium form of the Ffowcs Williams–Hawkings equation. Calculations are presented for a reference case of a four-bladed low-speed propeller in forward flight. The acoustic predictions are supple…

Magneto-electric laminates free vibration characterization by dual reciprocity BEM

Analytical solution for Magneto-Electro-Elastic Bimorph

Hierarchical BEM for dynamic analysis of anisotropic 3-D cracked solids

Grain-boundary modelling of hydrogen assisted intergranular stress corrosion cracking

Abstract A novel hybrid strategy for modelling intergranular hydrogen embrittlement in polycrystalline microstructures is proposed. The technique is based on a grain-boundary integral representation of the polycrystalline micro-mechanics, numerically solved by the boundary element method, coupled with an explicit finite element model of the intergranular hydrogen diffusion. The intergranular interaction between contiguous grains in the aggregate is modelled through extrinsic cohesive-frictional traction-separation laws, whose parameters depend on the concentration of intergranular hydrogen, which diffuses over the interface according to the Fick’s second law, inducing the weakening of the i…

Structural Health Monitoring Procedure for Composite Structures through the use of Artifcial Neural Networks

In this paper different architectures of Artifcial Neural Networks (ANNs) for structural damage detection are studied. The main objective is to investigate an ANN able to detect and localize damage without any prior knowledge on its characteristics so as to serve as a real-time data processor for Structural Health Monitoring (SHM) systems. Two different architectures are studied: the standard feed-forward Multi Layer Perceptron (MLP) and the Radial Basis Function (RBF) ANNs. The training data are given, in terms of a Damage Index =D, properly defined using a piezoelectric sensor signal output to obtain suitable information on the damage position and dimensions. The electromechanical respons…

Wing pitching and loading with propeller interference

Virtual Element Method: Micro-Mechanics Applications

In this contribution we present an application of the lowest order Virtual Element Method (VEM) to the problem of material computational homogenization. Material homogenization allows retrieving material properties through suitable volume averaging procedures, starting from a detailed representation of the micro-constituents of the considered material. The representation of such microstructure constitutes a remarkable effort in terms of data/mesh preparation, especially when there is not evident microstructural regularity. For such a reason, computational micromechanics may represent a challenging benchmark for showing the potential of VEM. In this contribution, polycrystalline materials ar…

MITC FINITE ELEMENTS FOR MAGNETO-ELECTRO-ELASTIC PLATES BASED ON EQUIVALENT SINGLE-LAYER THEORY

Finite elements for magneto-electro-elastic laminated plates are formulated. They are based on an equivalent single-layer model, which assumes the first order shear deformation theory and quasi-static behavior for the electric and magnetic fields. To infer the plate model, the electro-magnetic state is firstly determined and condensed to the the mechanical primary variables, namely the generalized displacements. In turn, this result is used into the layers constitutive law to obtain the equivalent single-layer laminate constitutive relationship that expresses the plate mechanical stress resultants in terms of the generalized displacements taking the magneto-electro-elastic couplings into ac…

Variable kinematics equivalent single layer theories for magneto-electro-elastic multilayered plates

In recent years, the employment of smart materials able to provide multi-functional capabilities, besides the traditional structural functions, has been gaining attention in several technological fields (automotive, aerospace, biomedical, robotics, etc.). This possibility of coupling different physical fields can be and it has been exploited in transducer applications, structural health monitoring, vibration control, energy harvesting and other applications. In this framework, magneto-electro-elastic (MEE) materials are attracting increasing consideration from academic and industrial audiences: MEE materials have the ability to couple mechanical, electrical and magnetic fields and this make…

X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks

The analysis of large amplitude vibrations of cracked plates is considered in this study. The problem is addressed via a Ritz approach based on the first-order shear deformation theory and von Karman’s geometric nonlinearity assumptions. The trial functions are built as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour (which motivates why the method is dubbed as eXtended Ritz); boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions along the plate edges. Convergence and accuracy are assessed to validate the approach and show its efficiency and potential. Original results are then…

A finite element formulation for large deflection of multilayered magneto-electro-elastic plates

An original finite element formulation for the analysis of large deflections in magneto-electro-elastic multilayered plates is presented. The formulation is based on an equivalent single-layer model in which first order shear deformation theory with von Karman strains and quasi-static behavior for the electric and magnetic fields are assumed. To obtain the plate model, the electro-magnetic state is firstly determined and condensed to the mechanical primary variables, namely the generalized displacements. In turn, this result is used to obtain laminate effective stiffness coefficients that allow to express the plate mechanical stress resultants in terms of the generalized displacements and a…

Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates

In this work, a novel high-order formulation for multilayered piezoelectric plates based on the combination of variable-order interior penalty discontinuous Galerkin methods and general layer-wise plate theories is presented, implemented and tested. The key feature of the formulation is the possibility to tune the order of the basis functions in both the in-plane approximation and the through-the-thickness expansion of the primary variables, namely displacements and electric potential. The results obtained from the application to the considered test cases show accuracy and robustness, thus confirming the developed technique as a supplementary computational tool for the analysis and design o…

Explicit Kutta Condition for Unsteady Two-Dimensional High-Order Potential Boundary Element Method

An explicit unsteady pressure Kutta condition is discribed that was directly and efficiently implemented in a time domain high-order potential panel method so as to ensure the pressure equality on the upper and lower surfaces at the trailing edge of the airfoil at each time step.

Boundary-layer effects in wedges of piezoelectric laminates

An approach to investigate boundary-layer effects in wedges of piezoelectric laminated structures is presented with the aim of ascertaining the electromechanical response characteristics. The wedge layer behavior is described in terms of generalized stress functions, which lead to a model consisting of a set of three coupled partial differential equations. The strength of the solution singularity is determined by solving the eigenvalue problem associated with the resolving system. The solution of the model is obtained by an eigenfunction expansion method coupled with a boundary collocation technique. Correspondingly, the singularity amplitude is assessed by introducing and calculating the g…

Global/Local FEM-BEM stress analysis of damaged aircraft structures

In this paper a Hierarchical approach for the analysis of advanced aerospace structures is presented. The proposed Global/Local model uses two kind of numerical methods. The first step of the Hierarchical procedure is performed by the Finite Element code Patran/Nastran™, using a coarse mesh to study the global structure, then the local region is analyzed by using a Boundary Element code based on the multidomain anisotropic technique. This code accurately predicts stress concentrations at crack tips with a reduction of the modeling efforts and of the computational time. The Global/Local interface code implemented allows an intuitive extraction of the local region with a substantial reduction…

An alternative BEM for fracture mechanics in orthotropic materials

Nonlocal model for a magneto-electro-elastic nanoplate

A mathematical model based on nonlocal third-order shear deformation plate theory has been developed to evaluate the mechanical and electromagnetic behavior of magneto-electro-elastic nanoplates. Two types of magneto-electro-elastic composites have been considered, all of them combination of Barium Titanate sheets, that represents the piezoelectric phase, and Cobalt Ferrite, that is the piezomagnetic component. Setting magneto-electric boundary conditions on each laminate, it has been possible to extrapolate and to analyze free vibrations frequencies for all considered plates, allowing to do objective assessments on what factors influence laminate modes and, especially, how these vary in th…

Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous elliptic operators

In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansions…

A fast hierarchical BEM for 3‐D anisotropic elastodynamics

A model for multilayered beams undergoing end loads

A formulation for layered beams undergoing end loads, namely axial, shear and bending actions, is developed and presented in this paper. A layer-wise kinematical model is first derived so that the point-wise balance relationships are fulfilled at the layer level. Successively, by enforcing the interface continuity conditions and taking the traction–free conditions on the top and bottom surfaces of the laminate into account, the layer-wise kinematical quantities are written in terms of generalized kinematical variables representative of the beam displacements field. The beam problem is then formulated in terms of these generalized variables leading to a model that shows the positive characte…