形状优化设计的一个方法——带参数的状态空间可行方向法

AN ALGORITHM OF THE SHAPE OPTIMAL DESIGN-STATE SPACE FEASIBLE DIRECTION ALGORITHM WITH PARAMETERS

本文用状态变量描述结构的性态约束,用参变量描述结构几何区域由形状设计变量的变化所产生的增量场,提高了敏度分析的计算效率,弥补了用有限差分法计算敏度的不足,构造了带参数的状态空间可行方向法,用来解平面应力(应变)结构形状优化设计问题,对所算例题,只要一、二次迭代分析,就可取得满意结果,附录给出了几个导数的表示。

In this paper, the nature constraints of a structure is described by the state variables, the incremental field of a structure geometrical area, which is resulted by a change of the shape design variable, is described by a parameter. Thus the efficiency of calculation in sensitivity analysis can be raised, and the defect of using finite difference approximation in calculating the sensitivity is remedied. The state space feasible direction algorithm with parameters is presented. It is applied to solve the shape optimal design problems of a plane continuous structure. For the examples given in paper, it has only need of once or twice iterations, a satisfied result can be obtained. In appendix some of derivatives are given.