基于连续密度变量的结构支撑布局优化设计

支撑布局的优化设计是决定结构设计质量与力学品质的关键因素 ,论文提出了用拓扑优化技术进行支撑布局优化设计的一种方法。为了实现结构动力学性能优化 ,采用拓扑优化方法中的虚拟密度技术 ,将支撑单元布局这一离散变量问题转化为连续变量优化问题。该方法以虚拟密度作为设计变量 ,基于单元刚度矩阵与设计变量的指数对应关系 ,建立了结构固有频率对设计变量的灵敏度计算格式 ,实现了动力学优化。论文给出了支撑布局拓扑优化的实例 ,这些问题对于检验论文中所使用的拓扑优化方法的可行性和结果的可信度有很大帮助 ,同样对于这种方法的推广应用也有很大指导意义。计算结果表明 ,拓扑优化方法不仅能够解决结构布局优化设计问题 ,而且在模型建立合理的情况下 ,也能够有效地对支撑布局进行动力学优化

Optimal Layout of Structural Support Conditions Based Upon Continuous Density Variables

The optimal layout of supports is the key factor t hat dominates the static and dynamic performances of the structure. The purpose of this work is to carry out layout optimization of supports by means of topolog y optimization. To have an easily solved problem formulation, the technique of i ntroducing pseudo-density variables is used, which transforms a discrete-varia ble problem into a continuous one. Based on this formulation, the relation betwe en the element stiffness matrix and density variable is described by a power law . The latter enables to establish the computing scheme of sensitivity analysis f or eigenfrequency. Problems associated with support layout optimization are solv ed. The first example is classical in structural mechanics. It is helpful to val idate the proposed approach. Other examples are more realistic from the engineer ing viewpoint. Solution results have a direct impact upon the practical applicat ions. Numerical results show that topology optimization is not only able to deal with layout design of structures, but also able to deal with problems of suppor t layout if the modeling is made reasonably.