Topology optimization of nonlinear structures with multiple materials using meshfree method and level set method

An enhanced meshfree methods combined with level set method are employed to solve the topology optimization problems of nonlinear structures made of multiple materials under large deformations. Moving Least Square Approximation (MLSA) with discontinuous derivatives basis function is used in order to treat the moving material interface represented by level set method during the procedures of topology optimization. The enhanced MLSA formulation provides meshfiree methods with the ability to handle the material discontinuity at the material interface accurately and efficiently, which can accurately and automatically solve the stress discontinuities around moving material interfaces. The numerical results show the success and accuracy of the present method by solving several 2-D topology optimization problems, involving single material structures and multiple materials structures, especially the structures made of nearly incompressible rubber-like materials undergoing large deformations.