Search results for "boundary element method."
showing 10 items of 158 documents
Closed form coefficients in the Symmetric Boundary Element Approach
2006
Abstract In the area of the structural analysis, the problems connected to the use of the symmetric Galerkin Boundary Element Method (SGBEM) must be investigated especially in the mathematical and computational difficulties that are present in computing the solving system coefficients. Indeed, any coefficient is made by double integrals including often fundamental solutions having a high degree of singularity. Therefore, the related computation proves to be difficult in the solution. This paper suggests a simple computation technique of the coefficients obtained in closed form. Using a particular matrix, called ‘progenitor’ matrix [Panzeca T, Cucco F, Terravecchia S. Symmetric boundary elem…
A boundary min-max principle as a tool for boundary element formulations
1991
Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.
On the Computational Aspects of a Symmetric Multidomain Boundary Element Method Approach for Elastoplastic Analysis
2011
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 SBEM approach, 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…
Domain decomposition in the symmetric boundary element analysis
2002
Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface boundary unknowns to the external actions. These relations, valid for e…
Multidomain boundary integral formulation for piezoelectric materials fracture mechanics
2001
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…
Application of the 3-D boundary element method to delaminated composite structures
2013
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…
Stress fields by the symmetric Galerkin boundary element method
2004
The paper examines the stress state of a body with the discretized boundary embedded in the infinite domain subjected to layered or double-layered actions, such as forces and displacement discontinuities on the boundary, and to internal actions, such as body forces and thermic variations, in the ambit of the symmetric Galerkin boundary element method (SGBEM). The stress distributions due to internal actions (body forces and thermic variations) were computed by transforming the volume integrals into boundary integrals. The aim of the paper is to show the tension state in Ω∞ as a response to all the actions acting in Ω when this analysis concerns the crossing of the discretized boundary, thu…
The development of a hybrid technique employing the boundary element method for thermoelastic stress separation
2000
: This paper presents a development of a hybrid technique employing a boundary element method for determining individual stress components in two-dimensional arbitrarily shaped domains from experimental isopachics only. The procedure consists of a numerical solution of two Poisson equations representing equilibrium for two-dimensional plane-stressed solids with zero body forces. An existing technique is employed for smoothing interior thermoelastic data and enhancing boundary information. The algorithm of stress separation has been implemented with the help of commercial codes. The whole procedure has been tested through a complete post-processing example of thermoelastic stress analysis da…
Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions
2016
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…