Search results for " Boundary element method"
showing 6 items of 46 documents
On the computational aspects of a symmetric multidomain BEM for elastoplastic analysis
2012
The symmetric boundary element method (SBEM) is applied to the elasto-plastic analysis of bodies subdivided into substructures. This methodology is based on the use of: a multidomain SBEMapproach, for the evaluation of the elastic predictor; a return mapping algorithm based on the extremal paths theory, for the evaluation of inelastic quantities characterizing the plastic behaviour of each substructure; and a transformation of the domain inelastic integrals of each substructure into corresponding boundary integrals. The elastic analysis is performed by using the SBEM displacement approach, which has the advantage of creating system equations that only consist of nodal kinematical unknowns a…
A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems
2010
In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…
A fast dual boundary element method for 3D anisotropic crack problems
2009
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 …
Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous 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 expansions…
Piezoelectric bimorph response with imperfect bonding conditions
2008
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…
BEM analysis of a piezoelectric structural health monitoring system for delamination detection
2013
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 …