Interface tracking in meshfree methods and its applications

Abstract

An enhanced meshfree method, moving least squares approximation with discontinuous derivative basis functions (MLSA-DBF), has been proposed in order to accurately track the derivative discontinuities of continuum or structures. Firstly, quadratic basis functions for MLSA-DBF in three dimensions are presented and the meshfree formulations in Cartesian coordinates are introduced for the analysis of shell structures with slope discontinuities. Numerical examples demonstrate the validity, accuracy, and convergence properties of the proposed method. Secondly, topology optimization with nonlinear materials under large deformation is established based on MLSA-DBF and the level set method. MLSA-DBF can achieve accurate stress and strain fields and obtain accurate sensitivity analysis in the topology optimization problems with fixed/moving material interfaces. The numerical results give faster convergence rate than the method without treatments for material interfaces, and show superior advantages for large deformation problems. It is shown that MLSA-DBF, which is a simple, universal and accurate method without extra parameters, can accurately track not only the material interfaces but also the slope discontinuities and even moving interfaces.