基于ICM方法的层合板结构流固耦合频率约束拓扑优化

该文基于独立、连续、映射(independent continuous mapping, ICM)的拓扑优化方法,针对层合板结构频率约束下流固耦合的拓扑优化问题进行了建模与求解。利用格林公式与瑞利商,进行了优化模型频率约束的显式化,并基于泰勒线性近似的方法推导了设计灵敏公式,同时采用对偶序列二次规划求解了该模型。另外,通过引入修正的Heaviside函数对拓扑变量进行了离散化处理。利用PCL(Patran Command Language)二次开发平台对现有MSC.Patran软件进行二次开发,并通过MSC.Nastran软件求解器,实现了优化算法。数值算例证明了该文程序与算法的有效性与可行性。

TOPOLOGICAL OPTIMIZATION OF LAMINATED PLATE SUBJECT TO FLUID-STRUCTURE INTERACTION WITH FREQUENCY CONSTRAINT BASED ON ICM METHOD

A topology optimization model for a laminated plate subjected to fluid-structure interactions with frequency constraints is established and solved based on ICM (Independent Continuous Mapping) method. An explicit expression of the frequency-constraint(s) with respect to the topological variables is obtained by using Green formula and Rayleigh quotient. The design sensitivity formula is deduced by taking the advantage of Taylor linear approximation. The mathematical model of this optimization is solved by dual sequential quadratic programming. In addition, a modified Heaviside function is introduced to deal with the discretization of topology variables. The optimal model and its algorithm have been implemented by using the development language of MSC. Patran and MSC. Nastran software. Numerical examples show the reliability and validity of the program and algorithm.