基于拓扑描述函数的连续体结构拓扑优化方法

A NEW TOPOLOGY DESCRIPTION FUNCTION BASED APPROACH FOR STRUCTURAL TOPOLOGY OPTIMIZATION ~1

提出了一种利用拓扑描述函数(TDF)作为拓扑设计变量求解连续体结构拓扑优化问题的新方法.优化问题的目标函数是结构的整体柔顺性,约束条件为对于可利用材料的体积限制.这种方法不仅可以消除拓扑优化中经常出现的棋盘格式等数值不稳定现象,而且能够有效地抑制传统算法处理此类优化问题时所引发的边界扩散效应.与其它的基于水平集描述函数的拓扑优化方法相比,所提出的算法不仅无需求解控制水平集函数演化的双曲守恒方程,而且合理地考虑了目标函数的拓扑导数信息,因而使得算法的计算效率有了显著的提高.

In the present paper, a new approach for structural topology optimization based on implicit topology description functions (TDF) is proposed. TDF is used to describe the shape/topology of the structure, which is approximated in terms of its nodal values. Then a relationship is established between the element stiffness and the values of the topology description function on its four nodes. In this way and with some non-local treatments of the design sensitivities, not only the shape derivative but also the topological derivative of the optimal design can be incorporated in the numerical algorithm in a unified way. Numerical experiments demonstrate that by employing this approach, the computational efforts associated with TDF (level set) based algorithms can be saved. Clear optimal topologies and smooth structural boundaries free from any sign of numerical instability can be obtained simultaneously and efficiently.