基于拓扑描述函数的特定性能材料设计方法

TOPOLOGY DESCRIPTION FUNCTION BASED METHOD FOR MATERIAL DESIGN

研究了拓扑描述函数在材料设计中的应用,给出了一种基于拓扑描述函数的特定性能材料设计问题的提法和求解方法.将拓扑描述函数表示成含参数的基函数之和,将材料微结构拓扑优化问题转化为设计基函数描述参数的尺寸优化问题,使问题求解更方便.基于拓扑描述函数的方法可以准确确定设计域上任意点的材料分布,避免了变密度法常出现的棋盘效应、设计变量和有限元单元相关的缺点;与传统的水平集方法相比,其优化模型可以利用现有的优化方法求解,避免了差分法求偏微分方程.具有正泊松比和负泊松比的特定弹性性能材料的设计算例,说明了基于拓扑描述函数的材料设计方法的有效性.

The purpose of this paper is to investigate the application of topology description function （TDF） in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basic functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basic functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in variable density method is avoided. Compared with conventional level set method,the optimization problem can be solved simply by existing optimization techniques without the process to solve the ＂ Hamilton-Jacobi-type＂ equation by difference method. The proposed method is illustrated with two 2D examples. One gives the unit cell with positive Poisson＇s ratio,the other with negative Poisson＇s ratio. The examples show the method based on TDF is effective for material design.