Modified proportional topology optimization algorithm for multiple optimization problems

Three modified proportional topology optimization (MPTO) algorithms are presented in this paper, which are named MPTOc, MPTOs and MPTOm, respectively. MPTOc aims to address the minimum compliance problem with volume constraint, MPTOs aims to solve the minimum volume fraction problem under stress constraint, and MPTOm aims to tackle the minimum volume fraction problem under compliance and stress constraints. In order to get rid of the shortcomings of the original proportional topology optimization (PTO) algorithm and improve the comprehensive performance of the PTO algorithm, the proposed algorithms modify the material interpolation scheme and introduce the Heaviside threshold function based on the PTO algorithm. To confirm the effectiveness and superiority of the presented algorithms, multiple optimization problems for the classical MBB beam are solved, and the original PTO algorithm is compared with the new algorithms. Numerical examples show that MPTOc, MPTOs and MPTOm enjoy distinct advantages over the PTO algorithm in the matter of convergence efficiency and the ability to obtain distinct topology structure without redundancy. Moreover, MPTOc has the fastest convergence speed among these algorithms and can acquire the smallest (best) compliance value. In addition, the new algorithms are also superior to PTO concerning suppressing gray-scale elements.