Search results for "boundary element method."
showing 8 items of 158 documents
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…
Functional a posteriori error estimates for boundary element methods
2019
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.
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 …
COMPUTATIONAL HOMOGENIZATION OF POLYCRYSTALLINE MATERIALS WITH PORES: A THREE-DIMENSIONAL GRAIN BOUNDARY FORMULATION
2012
In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a 3D grain boundary micro mechanical model. The volume fraction of pores, their size and distribution can be varied to better simulate the response of real porous materials. The formulation is built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi Tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play …
Influence of the Resin Layer Thickness at the Interface of Hybrid Metal-composite Co-cured Joints
2011
As discussed in literature, the accurate analysis of the modern co-cured joints between composite materials or between a metal and a composite material (hybrid joints) is complicated by the influence of the interface resin layer on the interface singular stress field. In such joints, in fact, there is not a proper adhesive layer and the thickness of the resin layer, that plays the role of the adhesive, is not constant due to the presence of the reinforcing fibers in the composite adherent. For this reason several authors assume that a generic co-cured joint can not be studied as a simple bi-material joint, without considering the particular characteristics of the actual resin layer. This pr…