A Two Level Approximation Technique for Structural Optimization

Abstract

This work presents a method for optimum design of structures, where the design variables can he considered as Continuous or discrete. The variables are chosen as sizing variables as well as coordinates of joints. The main idea is to reduce the number of structural analyses and the overal cost of optimization. In each design cycle, first the structural response quantities such as forces, displacements, etc. are approximated as functions of the design variables or some intermediate variables. By employing these approximated quantities, an explicit approximate problem will be available, which is in general a nonlinear programming problem. Now, this approximate design task is transformed into a number of second level approximation of separable froms, each of which can be solved by a dual strategy with continuous or discrete variables. The objective of the first level approximation is to reduce the number of structural anlyses required in the optimization problem and that of the second level approximation is to reduce the computational cost of the optimization technique. Two examples are offered to demonstrate the efficiency and reliability of the proposed method.