Topology Optimization Method And Its Application Research Based On Mathematical Programming Solving

This paper mainly makes researches on structural topology optimization method dealing with mathematical programming solving, gives the algorithm and programs of the structural topology optimization method considering frequency constraints and considering displacement and frequency constraints. And a lot of numerical simulations are completed.Based on the ideas of the ICM method and the evolutionary structural optimization method, first, this paper proposes a new structural topological optimization method considering only displacement constraints. At the initial iteration step of each optimization iteration sub-loop, in order to control the change quantity of topological design variables, new constraint limits are formed and introduced into the optimization model. Moreover, the element deletion and adding criterion and a set of structural optimization strategies are given. Incorporating the Lagrange multiplier method, a set of solving method for continuous topological variables of sub-loop iterations is improved, and a new continuum structural topological optimization method considering only displacement constraints is proposed.Then, this paper has made researches on the structural topological optimization problem with the objective function being the structural weight and just considering frequency constraints, and considering displacement and frequency constraints based on mathematical programming solving.For the mentioned-above proposed methods their procedures are implemented, and a lot of typical structural design examples are given, and simulation designs of a truck frame structure and other components are completed. Results obtained show that the proposed methods in this thesis are correct and efficient, and are of good engineering application value.