A structural topological optimization method for multi-displacement constraints and any initial topology configuration

In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be 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 distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.

A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

基于独立连续映射法的位移约束梯度点阵结构轻量化拓扑优化

基于独立连续映射(ICM)方法提出一种以位移约束下体积最小为目标的梯度点阵结构拓扑优化设计新方法.首先采用基于应变能的均匀化方法分析了梯度单元的有效弹性特性.建立四次多项式插值的代理模型,将独立的连续拓扑变量映射到单元的有效弹性矩阵,建立了宏观结构与微观单元之间的关系.其次,建立轻量化拓扑优化模型,通过灵敏度分析将其转化为显式标准二次规划问题,并用对偶序列二次规划求解.数值算例表明,与均匀点阵结构相比,梯度点阵结构具有更好的轻量化效果,验证了该方法的有效性和可行性.结果表明,随着位移约束的增加,梯度点阵结构变得更轻.此外,还得到了一些不同的拓扑构型.该方法为梯度点阵结构设计提供参考,并扩展ICM方法的应用范围.