This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j. Each increase or decrease of {\phi}ij corresponds to a material change between the two materials. This approach reduces the dependence of the initial configuration in the optimization calculation and simplifies the sensitivity analysis. First, the topology optimization problem is formulated in the X-LS representation. Next, the reaction-diffusion equation that updates the level set function is introduced, and an optimization algorithm that solves the equilibrium equations and the reaction-diffusion equation using the fi- nite element method is constructed. Finally, the validity and utility of the proposed topology optimization method are confirmed using two- and three- dimensional numerical examples.
翻译:本文为多种材料设计提供了一个基于扩展等级的优化表层设计法(X-LS) 。 在拟议方法中, 水平设定函数 {phi}ij 的每零级数据集代表材料i 和j之间的界限。 每增加或减少 {phi}ij 对应两种材料之间的实质性变化。 这种方法减少了初始配置在优化计算中的依赖性, 并简化了敏感度分析。 首先, X- LS 表示中提出了地形优化问题 。 其次, 引入了更新级别设定函数的反弹扩散方程式, 并构建了使用 i- 硝元素方法解决平衡方程式和反弹扩散方程式的优化算法。 最后, 使用二维和三维数字示例确认了拟议表层优化方法的有效性和实用性。