The improved element-free Galerkin method for three-dimensional elastoplasticity problems

In this study, the improved element-free Galerkin (IEFG) method is presented to the three-dimensional elastoplasticity problems. The improved least-squares (IMLS) approximation is used to obtain the shape function, the Galerkin weak form of three-dimensional elastoplasticity problems considering the nonlinear stress strain relationship is used to form the discrete equation system, and penalty method is applied to the displacement boundary conditions, then the formula of the IEFG method for three-dimensional elastoplasticity problems are obtained. Some numerical examples are given to discuss the convergence of the IEFG method in this paper and the influences of the weight function, the scaling parameter, the penalty factor, the node distribution and the step number on the computational accuracy of the numerical solutions of the IEFG method. Comparing with the element-free Galerkin (EFG) method, the method in this study has a greater computational efficiency.