多层次结构优化方法

本文提出了—种包含虚节点和虚单元的力学模型。称为广义结构;导出了分析广义结构的公式;利用Kuhn-Tucker,条件和满应力准则分别建立了虚单元转为实单元的条件;利用这一条件,可以把结构拓扑优化的非线性规划由混合型转化为连续型,使问题的困难度大为降低。这是一种以单一的尺寸变量为变量的,适用于尺寸优化、几何优化和拓扑、布局优化等各个层次结构优化问题的方法,文内还讨论了用本方法得到的解与总极值的关系,并有几个算例说明方法的有效性。

A Method of Structural Optimization with Multi-Level

In this paper a new mechanical model called general structure which consists of basic structure, virtual elements and virtual nodes is presented. The formuale that are used to analyse the general structure are developed. Two criterions that can judge a virtural element converting into real one are developed with Kuhn-Tucker condition and the "F.S.M" respectively. With one of them the mixed nonlinear program of structure topological optimization is change to serial one. Thus, the degree of difficulties of the program is greatly reduced. This method takes the sectionof element as the sole type of design variable and is suitable to all levels of structural optimization. There are three examples to show the efficiency of the method.