频率约束板结构拓扑优化

本文利用ICM（独立、连续、映射）方法建立了频率约束下平板结构重量最轻的拓扑优化模型。采用指数函数作为单元重量、单元质量及单元刚度的过滤函数。通过瑞利商对刚度过滤函数倒变量的泰勒一阶展式，将频率约束近似显式化。利用对偶理论将含有大量设计变量的约束优化模型转化为易于求解的少设计变量拟无约束优化模型，通过序列二次规划将转化模型进行求解，提高了求解的效率。本文选择MSC.Patran&Nastran软件及PCL二次开发语言构架了平板结构频率约束拓扑优化问题的软件。数值算例表明：本文的方法具有迭代稳定性和收敛高效性。

TOPOLOGICAL OPTIMIZATION OF THE PLATE STRUCTURE SUBJECTED TO THE FREQUENCY CONSTRAINTS

In this paper,a model of topology optimization for the lightest plate structures with frequency constraint is constructed based on Independent,Continuous and Mapping(ICM) method.Exponential function is adopted as filtering function of the element weight,the element mass matrix and the element stiffness matrix.Through the first-order Taylor expansion of Rayleigh quotient,which is described by the reciprocal variables of the filtering function of the element stiffness,the frequency constraint is approximately expressed as an explicit function.The dual theory is used to convert the constrained optimization model with a large number of design variables into the quasi-unconstrained optimization model with less design variables,which is solved by the sequential quadratic programming(SQP).As a result,the solving efficiency is greatly improved.The MSC.Patran & Nastran software and Patran Command Language(PCL) are selected to develop the topology optimization software for plate structures with frequency constraint in there.The numerical results show that the ICM method possesses stable iteration and efficient convergence.