| 基于参数化水平集法的材料非线性子结构拓扑优化 |
| |
| 引用本文： | 雷阳,封建湖.基于参数化水平集法的材料非线性子结构拓扑优化[J].应用数学和力学,2021,42(11):1150-1160. |
| |
| 作者姓名： | 雷阳 封建湖 |
| |
| 作者单位： | 长安大学 理学院, 西安 710064 |
| |
| 基金项目： | 陕西省自然科学基金（2018JQ1027）；中央高校基本科研业务费(300102120107） |
| |
| 摘 要： | 针对利用传统水平集法进行非线性结构拓扑优化计算过程复杂及计算效率低等问题，将参数化水平集方法引入材料非线性结构拓扑优化中。通过全局径向基函数插值初始水平集函数，建立了以插值系数为设计变量、结构的应变能最小为目标函数、材料用量为约束条件的材料非线性结构拓扑优化模型，利用有限元分析对材料非线性结构建立平衡方程，并用迭代法求解。同时，采用子结构法划分设计区域为若干个子区域，将全自由度平衡方程的求解分解为缩减的平衡方程和多个子结构内部位移的求解，减小了计算成本。算例表明，这种处理非线性关系的方法可以在保证数值稳定的同时提高计算效率，得到边界清晰、结构合理的拓扑优化构形。
|
| 关 键 词： | 拓扑优化 参数化水平集法 非线性材料 子结构法 |
| 收稿时间： | 2021-04-07 |
Topology Optimization of Nonlinear Material Structures Based on Parameterized Level Set and Substructure Methods |
| |
| Affiliation: | School of Sciences, Chang’an University, Xi’an 710064, P.R.China |
| |
| Abstract: | In order to overcome the problems of complicated calculation process and lower computational efficiency of the traditional level set method (LSM), for nonlinear structure topology optimization, a parameterized level set method (PLSM) was introduced. Through interpolation of the initial level set function with the globally supported radial basis function (GSRBF), a nonlinear material structure topology optimization model was established with the interpolation coefficient as the design variable, the minimum strain energy of the structure as the objective function, and the material amount as the constraint condition. The equilibrium equation for the nonlinear material structure was established by finite element analysis, and solved with the iterative method. In addition, the substructure method (i.e. the domain decomposition method) was used to divide the design area into several sub-areas, and the solution to the full degree of freedom equilibrium equation was decomposed into a set of solutions of reduced equilibrium equations and solutions of multiple substructures’ internal displacements, which could reduce the computation cost. Examples show that, this method can ensure the numerical stability, improve the computational efficiency, and obtain the topology optimization configuration with clear boundaries and reasonable structures. |
| |
| Keywords: | |
|
| 点击此处可从《应用数学和力学》浏览原始摘要信息 |
|
点击此处可从《应用数学和力学》下载全文 |
|
