Floating stress‐point integration meshfree method for large deformation analysis of elastic and elastoplastic materials

Abstract

SUMMARY A new meshfree formulation of stress‐point integration, called the floating stress‐point integration meshfree method, is proposed for the large deformation analysis of elastic and elastoplastic materials. This method is a Galerkin meshfree method with an updated Lagrangian procedure and a quasi‐implicit time‐advancing scheme without any background cell for domain integration. Its new formulation is based on incremental equilibrium equations derived from the incremental virtual work equation, which is not generally used in meshfree formulations. Hence, this technique allows the temporal continuity of the mechanical equilibrium to be naturally achieved. The details of the new formulation and several examples of the large deformation analysis of elastic and elastoplastic materials are presented to show the validity and accuracy of the proposed method in comparison with those of the finite element method. Copyright © 2012 John Wiley & Sons, Ltd.

A Novel Finite Element Formulation for Large Deformation Analysis Based on Incremental Equilibrium Equation in Conjunction With Rezoning Technique

“…Meanwhile, we recently proposed a new Galerkin meshfree formulation based on the incremental equilibrium equation (IEE) [5]. The IEE was developed for Galerkin meshfree methods with the updated Lagrangean procedure to resolve the temporal discontinuity of the nodal internal force between the old and the new moving least square (MLS) supports, and it brought out high performances in stability and accuracy in large deformation analysis for elastic and elastoplastic bodies.…”

“…It would appear that this discontinuity issue is essentially identical to that in the FE rezoning method mentioned above. However, the IEE is still a semiempirical equation without any mathematical derivation [5] and verified only in the meshfree formulation. To derive the IEE mathematically and to apply it for the FE rezoning method should be important.…”