On Topology Optimization and Canonical Duality Method
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The general problem in topology optimization is correctly formulated as a double- 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 both 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.
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