基于拓扑描述函数的特定性能复合材料设计

A NEW TOPOLOGY DESCRIPTION FUNCTION BASED APPROACH FOR MATERIAL DESIGN WITH PRESCRIBED PROPERTIES

提出了一种基于拓扑描述函数进行特定性能复合材料设计的新方法.采用拓扑描述函数作为设计变量,把复合材料微结构的设计问题转化为一个在周期性单胞上的拓扑优化问题.拓扑描述函数以及相应正则化机制的引入不仅可以有效消除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.数值结果表明所提出的方法可以稳定高效地实现具有特定性能的复合材料微结构设计.

In the present paper, a new approach for the design of the microstructures of composite materials with prescribed properties 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 by finite element. Then a relationship is established between the element stiffness and the values of the topology description function on its four nodes. Some regularization techniques have also been introduced to make the process of optimization become more stable. Numerical experiments demonstrate that by employing this approach, the computational efforts associated with the solution of material design problems can be saved. Clear topologies of the material microstructures that are free from any sign of numerical instability can be obtained in an efficient way.