On Topology Optimization and Canonical Duality Method

The general problem in topology optimization is correctly formulated as a doublemin mixed integer nonlinear programming (MINLP) problem based on the minimum total potential energy principle. It is proved that for linear elastic structures, the alternative iteration leads to a Knapsack problem, which is considered to be NP-hard in computer science. However, by using canonical duality theory (CDT) developed recently by the author, this challenging 0-1 integer programming problem can be solved analytically to obtain global optimal solution at each design iteration. The novel CDT method for general topology optimization is refined and tested mainly by 2-D benchmark problems in topology optimization. Numerical results show that without using filter, the CDT method can obtain exactly 0-1 optimal density distribution with almost no checkerboard pattern. Its performance and novelty are compared with the popular SIMP and BESO approaches. A brief review on the canonical duality theory for solving a unified problem in multi-scale systems is given in Appendix.