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TOPOLOGY DESCRIPTION FUNCTION BASED METHOD FOR MATERIAL DESIGN

ISSN号：0894-9166
期刊名称：《固体力学学报：英文版》
时间：0
分类：O34[理学—固体力学;理学—力学]
作者机构：[1]State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China
相关基金：Project supported by the National Natural Science Foundation of China （No.10332010）, the Innovative Research Team Program （No.10421202）, the National Basic Research Program of China （No. 2006CB601205） and the Program for New Century Excellent Talents in Universities of China （2004）.

关键词：拓扑分析, 拓扑描述功能函数, 物质设计, TDF, topology optimization, topology description function, material design

中文摘要：

这篇论文的目的是在材料设计调查拓扑学描述功能(TDF ) 的应用程序。使用 TDF 与规定机械性质描述微观结构，明确的表达和材料的设计问题的解决的技术的拓扑学被介绍。由作为参数决定的一系列基础函数的和介绍 TDF，因为设计变量的一个尺寸优化问题是 TDF 基础函数和设计域的网孔的独立人士的参数，材料微观结构的拓扑学优化被提出。由这个方法，为在设计领域描述成分材料的分发的高质量的拓扑学能被获得，经常在可变密度方法遇见的棋盘问题被避免。与常规水平集合方法相比，没有这个过程，优化问题能被存在优化技术简单地解决解决“ Hamilton-Jacobi-type ”由差别方法的方程。建议的方法与二个 2D 例子被说明。一个人与积极泊松的比率给联合起来的房间，其它与否定泊松的比率。例子证明方法为材料设计基于 TDF 是有效的。

英文摘要：

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 basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis 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 the variable density method is avoided. Compared with the 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 the difference method. The method proposed 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.

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