基于物质点变量的连续体结构拓扑优化方法

项目名称： 基于物质点变量的连续体结构拓扑优化方法

项目编号： No.11202078

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 龙凯

作者单位： 华北电力大学

项目金额： 24万元

中文摘要： 连续体结构拓扑优化结果中普遍存在棋盘格和网格依赖性现象，采用合理的数学模型描述连续介质成为解决上述问题的新途径。不同于以单元或节点表征单元有无的方法，基于物质点变量的连续体结构拓扑优化方法从拓扑优化的本质出发，提出了用于描述物质点及其领域有无的物质点变量。本项目拟首先研究连续、光滑的拓扑变量场构造方式，以克服各类数值不稳定性问题；并采用新材料插值模型以提高静动态等优化问题效率和稳健性；在上述基础上，发展基于纯无网格法分析新拓扑优化方法和形状优化方法。项目思路新颖，并具有重要的理论和工程意义。

中文关键词： 拓扑优化；独立连续映射法；变密度法；节点变量；物质点变量

英文摘要： Checkerboard pattern and mesh independence prevail in various optimal topological configuration of continuum structures. Proper mathematics' description of continuum struture can be viewed as the new way to eliminate the above problems. Different with those method based on element or node variables, the material-point independent topological variable varying from zero to one denotes the inexistence or the existence of material point and its vicinity. The concept of topological variable is defined from the essence of topology optimization. In this project , the way of constructing the continuous and smooth topological variables field will be defined firstly to overcome the numerical instability. To improve the convergence for topology optimization of continuum structure, a new material interpolation model will be proposed. Based on the above research, some new topology and shape optimization methods combined with pure meshless method will be developed. Some new ideas can be reflected in this project. In the meantime, some important academic and engineering significance wiill be in this project.

英文关键词： topology optimization；independent continuous mapping method；variable density method；nodal variable；material point variable