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

摘要

A boundary element method (BEM) approach for the solution of the elastic problem with geometrical non-linearity is proposed. The geometrical non-linearity's that are considered are both finite strains and large displacements. Material non-linearity's are not considered in this paper, so the constitutive law employed is Hook's elastic one and the fundamental solution introduced in the integral equations is the usual one for isotropic linear elasticity. in order to deal with the intricate non-linear equations that govern the problem, an incrementaliterative 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 process is necessary in order to achieve a good approximation to the governing 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 standardized finite element method code.