Showing papers by "Federico París published in 2006"

Application of BEM to generalized plane problems for anisotropic elastic materials in presence of contact

Abstract: It is in many cases very instructive and useful to have the possibility of treating three-dimensional problems by means of two-dimensional models. It always implies a reduction in computing cost which is particularly significant in presence of non-linearities, derived for instance from the presence of contact between the solids involved in the problem. The term generalized plane problem is adopted for a three-dimensional problem in a homogeneous linear elastic cylindrical body where strains and stresses are the same in all transversal sections. This concept covers many practical cases (for instance in the field of composites), a particular situation called generalized plane strain (strains, stresses and displacements are the same in all transversal sections) being the most frequently analyzed. In this paper, a new formulation is developed in a systematic way to solve generalized plane problems for anisotropic materials, with possible friction contact zones, as two-dimensional problems. The numerical solution of these problems is formulated by means of the boundary element method. An explicit expression of a new particular solution of the problem associated to constant body forces is introduced and applied to avoid domain integrations. Some numerical results are presented to show the performance and advantages of the formulation developed.

On the removal of the non‐uniqueness in the solution of elastostatic problems by symmetric Galerkin BEM

Abstract: A study of the removal of the non-uniqueness in the solution of elastostatic problems by means of the symmetric Galerkin boundary element method is presented. The paper focuses on elastic problems defined on domains with cavities, where cavity boundaries are subjected to traction boundary conditions. A simple method consisting in a direct application of support conditions and several methods based on the Fredholm theory of linear operators are introduced, implemented and analysed. Numerical examples demonstrate the performance of the proposed methods and accuracy of their results, a comparative evaluation of the methods developed being finally presented. Copyright © 2005 John Wiley & Sons, Ltd.

Note on the removal of rigid body motions in the solution of elastostatic traction boundary value problems by SGBEM

Abstract: A study of errors appearing in traction boundary value problems on simply connected domains solved by the symmetric Galerkin boundary element method (SGBEM) is presented Two methods for the removal of rigid body motions from the nullspace of the discretised SGBEM system matrix, one based on the direct enforcement of additional point supports and the other based on the Fredholm theory of linear operators, are analysed The fulfillment of the global equilibrium conditions by the discretised load has been found to be the key point in the different behaviour of the errors in displacements obtained applying these two methods The main objective of this paper is to compare the application of these methods with the SGBEM and with the classical collocation BEM, clarifying in particular a different role of the equilibrium of the discretised load in the SGBEM and classical collocational BEM linear systems Conclusions of the theoretical analysis presented are confirmed by numerical examples, where the conditions of the global equilibrium are either fulfilled or slightly violated by the discretised load