基于隐含边界描述的连续体拓扑优化

基于隐含边界描述的水平集方程推动几何边界,结合形状导数、拓扑导数等工具,实现了柔性目标函数的连续体结构拓扑优化设计.进一步通过引入Von Mises应力作为产生新拓扑结构的策略,给出了单独使用Von Mises应力开孔的算例.算例结果表明,基于隐含边界描述的连续体拓扑优化设计方法,它具有独特的处理拓扑变化能力及消除拓扑优化结果对网格和初始拓扑结构猜测的依赖性.这一类方法具有优秀的高维设计拓展能力,在工程实际和多材料设计等方面具有很好的应用前景.

Continuum Structure Topology Optimization Based on Implicit Boundary Representation

This paper introduced a continuum structure topology optimization method based on implicit boundary representation,such as level set method.This method combines level set method,shape derivative analysis and topology derivative to realize structural topology optimization.Furthermore,Von Mises stress was used as an index to generate new topologies.Two numerical examples were given which shows that this kind of method has superior ability to handle topological change during optimization and is very effective to make topology optimization process independent of initial topological guess and mesh size.At the same time,this method has the capability to easily handle higher dimensional problems.It has great potential usage in industrial practice and multi-material topological design.