多层渐进黑白拓扑优化设计方法

提出一种多层渐进黑白(0-1)拓扑优化设计方法。采用SIMP方法松弛设计变量，利用灵敏度过滤消除棋盘格。将拓扑图中无效的中间单元看成多余材料，在此基础上，采用体积比多层延拓方案，逐步逼近优化问题的目标体积比，同时，利用基于相对密度的单元渐进筛选方法，分层地去除设计域中的无效材料，保留其中的最有效材料，并逐层缩小拓扑优化模型的可利用材料域。通过这种方式，使0-1拓扑设计转化为具有连续设计变量的多层渐进拓扑优化过程，从而最终得到满足目标体积比的黑白拓扑。最后，以柔性最小化及柔顺机构拓扑设计问题为例，进行了算法验证，结果表明该算法能够实现较好的0-1收敛效果。

Multi-level Evolutionary approach for the Black-and-white Topology Optimization Design

A multi-level evolutionary method for the 0-1 topology optimization design was proposed. The binary constraints on design variables were relaxed based on the scheme of  SIMP. And the checkerboards were filtered and removed by sensitivity. The ineffective intermediate elements were considered as redundant materials. Then, a multi-level continuation scheme on the volume ratio was used to approach the objective volume ratio of the optimization problem gradually. Meanwhile, based on relative densities an evolutionary screening strategy for elements was applied to remove ineffective materials in the design stratified, to remain the most effective materials, and to diminish the available material domains of topology optimization models with the changing layers. By this way, the 0-1 topology design was transformed into a multi-level evolutionary procedure of the topology optimization. Consequently, a preferable black-and-white topology satisfying the objective volume ratio could be obtained as expected. Finally, numerical examples of the topology design including compliance minimization and compliant mechanism problems were employed to verify the feasibility of the proposed method. The results demonstrate that the present method may achieve a relatively good 0-1 convergent effect.