A Novel Meshfree Method for Large Deformation Analysis of Elastic and Viscoelastic Bodies without Using Background Cells

Abstract

A Galerkin-type new meshfree formulation for large deformation analysis of elastic and viscoelastic bodies with a quasi-implicit time advancing scheme was proposed. The proposed method uses floating stress-points for the domain integration instead of background cell integration or nodal integration. The nodes and stress-points are initially arranged in the domain in a similar way of finite elements with coarseness and fineness. The number of stress-points is set greater than that of the nodes so that zero-energy modes don't arise unlike nodal integration methods without stabilization. Shape functions and their derivatives at each stress-points are defined by moving least squares (MLS) approximation with variable support radii and are updated in every time steps. A scaling-typed integration correction was introduced for the satisfaction of integration constraints. A patch test and beam bending analyses were performed to verify and evaluate the accuracy of the proposed method. Additionally, a press forming-like analysis that is difficult to be analysed with finite element methods without adaptive meshing technique was performed and successfully converged.