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…

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…

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 …

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

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

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…

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

Analytical solution for the transient response of symmetric magnetoelectric laminated beams

In this paper an analytical solution is presented for the forced vibration problem of magnetoelectric symmetric laminated beams. In deriving the mathematical model the Timoshenko’s beam theory is used and the electric and magnetic fields are assumed to be quasi-static. The model is written for a magnetoelectric sensing device by applying proper magnetoelectric boundary conditions on the beam top and bottom surfaces. The model highlights that the magneto-electro-mechanical couplings affect the bending stiffness and that the magnetoelectric inputs can be treated as equivalent bending moments. Forced vibration analyses are presented to assess the reliability of the solution.

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.

Piezoelectric patches for the active repair of delaminated structures

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…

Global/local Fracture Mechanics Analyses of Advanced Aerospace Structures

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…

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…

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…

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 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…

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 …

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 …

Magneto-electric laminates free vibration characterization by dual reciprocity BEM

Analytical solution for Magneto-Electro-Elastic Bimorph

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…

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…