考虑静动力学特性的材料结构一体化多目标优化设计

针对复合材料微结构的内部构型和宏观排布的可设计性,以结构基频最大和柔度最小加权系数为目标,将微结构设计和多尺度计算结合,建立了考虑静动力学特性的材料/结构一体化多目标优化设计模型,实现了相应的算法和算例.方法中引入了微观和宏观两个尺度上的独立密度变量,采用RAMP(Rational Approximation ofMaterial Properties)方法对密度进行惩罚,利用有限元超单元技术建立材料与结构的联系,通过规一化目标函数有效避免了不同性质目标函数的量级差异.通过算例,获得了静动态权重系数对结构拓扑构型和目标函数(宏观结构的柔度和基频)的影响规律.研究结果表明:该方法是有效的,可作为对轻质结构进行静动态多目标优化设计的一种新方法.

INTEGRATED OPTIMIZATION DESIGN OF MATERIALS AND STRUCTURES IN CONSIDERATION OF STATIC AND DYNAMIC PERFORMANCES

It is well known that structural behaviors of composites are dictated by micro configuration and macro arrangement of microstructure. A multi-objectives optimization design model integrating materials and structures in consideration of static and dynamic performances for periodical composites is presented and related numerical experiments are carried out. In the model, the optimization objects are to maximize the structure fundamental frequency and minimize the structure compliance. RAMP (Rational Approximation of Material Properties) is adopted to ensure clear topologies in both macro and micro scales and design variables for macrostructure and microstructures are defined separately and integrated into one system by using the super-element technique. In addition, to improve the smoothness of the objective function and avoid the singularity of numerical computation, the weighted objection function is normalized. On the basis of the numerical experiments, the effects of the weighted coefficient of the static and dynamic optimization on the topology form and objective values (the structure fundamental frequency and compliance) are investigated. The results indicate that the proposed method is effective and can be used as an innovative design concept for lightweight structures.