Multiparameter structural optimization using FEM and multipoint explicit approximations

A unified approach to various problems of structural optimization, based on approximation concepts, is presented. The approach is concerned with the development of the iterative technique, which uses in each iteration the information gained at several previous design points (multipoint approximations) in order to better fit constraints and/or objective functions and to reduce the total number of FE analyses needed to solve the optimization problem. In each iteration, the subregion of the initial region in the space of design variables, defined by move limits, is chosen. In this subregion, several points (designs) are selected, for which response analyses and design sensitivity analyses are carried out using FEM. The explicit expressions are formulated using the weighted least-squares method. The explicit expressions obtained then replace initial problem functions. They are used as functions of a particular mathematical programming problem. Several particular forms of the explicit expressions are considered. The basic features of the presented approximations are shown by means of classical test examples, and the method is compared with other optimization techniques.Presented at NATO ASI Optimization of Large Strucutral Systems, held in Berchtesgarden, Germany, Sept. 23 — Oct. 4, 1991