A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method

Abstract

The topology optimization of a linearized elasticity system with the area (volume) constraint is investigated. A non-ersatz material approach is proposed. By introducing a fixed background domain, the linearized elasticity system is extended into the background domain by a characteristic function. The piecewise constant level set (PCLS) method is applied to represent the original material region and the void region. A quadratic function of PCLS function is proposed to replace the characteristic function. The functional derivative of the objective functional with respect to PCLS function is derived, which is zero in the void region and nonzero in the original material region. A penalty gradient algorithm is proposed. Four numerical experiments of 2D and 3D elastic structures with different boundary conditions are presented, illustrating the validity of the proposed algorithm.