结构优化中的混合变量应力约束近似方法

MIXED VARIABLES APPROXIMATION METHOD FOR STRESS CONSTRAINTS IN STRUCTURAL OPTIMIZATION

提出一种处理结构优化应力约束的新近似方法。以往一般直接对应力约束按设计变量近似,本文用近似内力间接近似应力约束以得到更高的近似质量。根据对内力和设计变量关系分析,提出了内力按混合变量一阶泰勒展开的高质量近似方法。近似优化问题用约束变尺度法求解。最后给出了几个典型例题,结果表明该方法简单、有效、可靠。

A new approximation method for dealing with stress constraints in structural optimization is presented. In previous method, it has been common to create directly an approximation of stress constraints with respect to the design variables. In present method, the stress are, instead indirectly approximated by approximated internal force of the member to make the approximate quality better. Based on analysing to relationship between the force and the desgin variables, It is proposed that the force is approximated by the first Taylor series expansion in terms of the mixed variables, which is of high quality. The approximated problem is solved by variable metric method for constrained optimization. Finally, typical examples are offered and compared with publised results, which show the method is simple, efficient and reliable.