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.