The 2-D plane strain analysis of elastic material and rigid plastic material using Element Free Galerkin method is presented. In addition, a parallel approach of elastic analysis using EFG method is presented. Linear polynomial basis and quartic spline weight function with circular domain of influence are used to constitute EFG shape function. Weight functions which are modified by auxiliary weight functions are used to impose essential boundary condition. Preconditioned conjugate gradient algorithm is employed for parallelization. In parallel approach, MPI is used for message passing. Integration points are uniquely defined on separate processors and node informations are shared with all processors so that all influenced nodes for each point can be defined locally on the corresponding processor. The effectiveness of the procedure is demonstrated by a couple of elastic examples.
In rigid plastic analysis, Lagrangian weight functions are constructed using material coordinate. The spatial derivatives of the Lagrangian shape functions involved in the stress computation of path dependent materials are calculated by an inverse mapping that requires the inversion of the deformation gradient.
