Search results for "Boundary element method."

Boundary element modeling and analysis of adhesive bonded structural joints

2007

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…

Micro-cracking of brittle polycrystalline materials with initial damage

2016

In this paper, the effect of pre-existing damage on brittle micro-cracking of polycrystalline materials is explored. The behaviour of single and multiple cracks randomly distributed within a grain scale polycrystalline aggregate is investigated using a recently developed grain boundary 3D computational framework. Each grain is modelled as a single crystal anisotropic domain. Opening, sliding and/or contact at grain boundaries are modelled using nonlinear cohesive-frictional laws. The polycrystalline micro-morphologies are generated using Voronoi tessellation algorithms in combination with a regularisation scheme to avoid the presence of unnecessary small geometrical entities (edges and face…

A Variational Approach to Boundary Element Methods

1988

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

2000

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…

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

2017

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…

Determination of Torsional Stresses in Shafts: From Physical Analogies to Mathematical Models

2015

This paper presents the historical development of methods used for the study of torsional stresses in shafts. In particular, the paper covers both analog methods, especially those based on electrical analogies proposed circa 1925, and numerical methods, especially finite difference methods (FDM), finite element methods (FEM) and boundary element methods (BEM).

Elastoplastic analysis by active macro-zones with linear kinematic hardening and von Mises materials.

2014

In this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von Mises materials under plane strain conditions is shown. The proposed approach works with the Symmetric Galerkin Boundary Element Method applied to multidomain problems using a mixed variables approach, to obtain a more stringent solution. The elastoplastic analysis is carried out as the response to the loads and the plastic strains, the latter evaluated through the self-equilibrium stress matrix. This matrix is used both, in the predictor phase, for trial stress evaluation and, in the corrector phase, for solving a nonlinear global system which provides the elastoplastic solution of the active…

Numerical model of macro-segregation during directional crystallization process

1998

Abstract In the paper the mathematical model of macro-segregation proceeding during the directional crystallization process is presented. The boundary-initial problem considered is discussed. Next the numerical approximation constructed on the basis of the boundary element method supplemented by a procedure called the artificial heat source method is described. The boundary condition on the solidification front resulting from the alloy component balance is introduced, while in finally the practical aspects of computations concerning the course of the process are discussed.

A fast 3D dual boundary element method based on hierarchical matrices

2008

AbstractIn this paper a fast solver for three-dimensional BEM and DBEM 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. Special algorithms are developed to deal with crack problems within the context of DBEM. The structure of DBEM matrices has been efficiently exploited and it has been demonstrated that, since the cracks form only small parts of the whole structure, the use of hierarchical matrices can be particula…

Boundary Element Crystal Plasticity Method

2017

A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and har…