An efficient structural topological optimization method for continuum structures with multiple displacement constraints

An efficient structural topological optimization method is proposed in this paper to obtain a well defined final design with multi-displacement constraints. In the proposed method, the whole optimization process is divided into two optimization phases and a phase transferring step. An optimization model is developed to deal with the varied displacement limits, design space adjustments, and reasonable relations between any element stiffness matrix, weight and its element topology variable. A procedure is then proposed to solve the optimization problem formulated in the first optimization phase. The design space is automatically adjusted when the design domain needs expansions. The final topology obtained by the proposed procedure in the first optimization phase can get close to the vicinity of the optimum topology. Another algorithm, in which element hard kills are incorporated, is given to improve the optimization efficiency and make the designed topology black/white in both the phase transferring step and the second optimization phase. Topology variable history information and a quadratic programming algorithm are adopted to reduce the number of heuristic parameters in this algorithm. The optimum topology can be easily obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design, and the computational efficiency is enhanced by reducing the element number of the design structural finite model in two optimization phases. And the examples also show that this method is robust and practicable.