A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method (Communications in Computational Physics, 2021)
The topology optimization of a linearized elasticity system with the area(volume) constraint is investigated. A non-ersatz material approach is proposed. Byintroducing a fixed background domain, the linearized elasticity system is extendedinto the background domain by a characteristic function. The piecewise constant levelset (PCLS) method is applied to represent the original material region and the voidregion. A quadratic function of PCLS function is proposed to replace the characteristicfunction. The functional derivative of the objective functional with respect to PCLSfunction 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 of2D and 3D elastic structures with different boundary conditions are presented, illustrating the validity of the proposed algorithm.
Keywords: Non-ersatz material approach; piecewise constant level set method; linearized elasticity system; sensitivity analysis; penalty gradient algorithm.