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.