频率约束的三维连续体结构动力拓扑优化设计

DYNAMIC TOLOGICAL OPTIMAL DESIGN OF THREE-DIMENSIONAL CONTINUUM STRUCTURES WITH FREQUENCIES CONSTRAINTS

针对频率约束和结构重量最小的动力拓扑优化问题,基于(independent continuous mapping,ICM)独立、连续、映射方法,建立了频率约束下的三维连续体拓扑优化模型.利用瑞利商和—阶泰勒展式对频率约束进行了显式化处理,并采用幂函数与复合指数函数作为过滤函数,将优化模型进行了标准化转换,利用对偶理论及数学规划法进行了求解.另外,利用质量矩阵和刚度矩阵过滤函数比值与动态约束处理了局部模态和模态交换等数值问题.最后,通过应用两类不同过滤函数的数值算例表明了文中模型及方法在处理动力拓扑优化问题上的合理性与有效性.

The purpose of present work is to study structural optimal design of dynamics for three-dimensional （3D） continuum structures, and to aim at constructing topological optimal formulation by using ICM method, which is considering weight as object function and fundamental eigenfrequency as constraints. An explicit ex- pression of frequency-constraint（s） with respect to topological variables is obtained based on Rayleigh＇s quotient and first-order Taylor expansion. And two types of models with filter functions including power function and exponential function are standardized. As a result, the topology optimization problem is solved by the dual quadratic programming. Localized mode and mode switching often occurred in structural optimization with natural frequency constraints are handled by using filter functions and moving constraints in the optimal pro- cess. Finally, several numerical examples applying different filter functions in the optimal model axe analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.