Nonlinear analysis of plates and laminates using the element free Galerkin method

A meshless method based in a Galerkin formulation, the element-free galerkin method (EFGM), has been extended for the use in the elastic and elasto-plastic analysis of anisotropic symmetric laminates. A Reissner–Mindlin plate theory, which is a first-order shear deformation theory (FSDT) is considered and briefly described in order to define the displacement field and the strain field. The approximation functions are calculated considering a moving least squares (MLS) approach which is consistent provided the basis is complete in the polynomials up to a desired order. A modified version of the Newton–Rapson method is used for the solution of the nonlinear system of equations and an anisotropic yield surface, Hill yield surface, is considered. The elasto-plastic algorithm of solution is described. Several problems of laminate bending are solved and the obtained solutions are compared with finite element solutions which show that the meshless approach developed is an alternative to the finite element method (FEM) for the solution of problems with material nonlinearity.