2D analysis for geometrically non-linear elastic problems using the BEM

A boundary element method (BEM) approach for the solution of the elastic pr oblem with geometrical non-linearities is proposed. The geometrical non-lin earities that are considered are both finite strains and large displacement s. Material non-linearities are not considered in this paper, so the consti tutive law employed is Hooke's elastic one and the fundamental solution int roduced in the integral equations is the usual one for isotropic linear ela sticity. In order to deal with the intricate non-linear equations that gove rn the problem, an incremental-iterative method is proposed. The equations are linearized and a Total Lagrangian Formulation is adopted. The integral equations of the BEM are developed in an incremental form. The iterative pr ocess is necessary in order to achieve a good approximation to the governin g equations. The problem of a slab under homogeneous deformation is solved and the results obtained agree with the analytical solution. The problem of a hollow cylinder under internal pressure is also solved and its solution compared with that obtained by a standardized finite element method code. ( C) 1999 Elsevier Science Ltd. All rights reserved.