Gradient and dilatational stabilizations for stress‐point integration in the element‐free Galerkin method

Abstract

AbstractStabilized stress‐point integration schemes based on gradient stabilization and dilatational stabilization methods are presented for linear elastostaticity problems in the framework of element‐free Galerkin (EFG) method. The instability in stress fields associated with the stress‐point integration is treated by the addition to the Galerkin weak form of stabilization terms which contain product of the gradient of the residual or the trace of the gradient of the residual; the latter is called dilatational stabilization. Numerical results show that the oscillations in the stress fields are successfully removed by the presented stabilization methods, and that the convergence and stability properties of direct stress‐point integration are greatly improved. These stabilization methods are particularly suitable for the solution of non‐linear continua with explicit time integration methods. Copyright © 2008 John Wiley & Sons, Ltd.