基于包络函数和二级近似概念的结构优化方法

利用包络函数、二级近似概念和对偶理论,提出了一种结构优化的有效解法.首先,利用包络函数将原多约束结构优化问题转化为单约束优化问题,再利用本文提出的新的两点近似函数构成高精度近似问题,继而用二级近似求解策略和对偶理论求解.理论与算例皆表明本方法的主要优点是其通用性和高的计算效率,这对于工程中的具有复杂函数的大型优化问题特别重要.

Structural Optimization Based on Envelope Function and Two-Level Approximation Concepts

An efficient solution method for structural optimization is proposed by coordinated use of mathematical transformation, two level approximation concepts and dual theory. At first the original multi constraint structural optimization problem is converted into a single constraint optimization problem by using envelope function which is then approximated by a new two point approximation function proposed in this paper, and then a corresponding high accuracy approximation problem is constructed. The solution of the approximation problem is obtained by two level strategy and dual theory. Theory and computation examples have shown that the main advantages of methods developed in the paper are the generality in use and the efficiency in computation, which are particularly important for large scale problems with complicated functions in engineering.