Efficient Optimum Design of Structures with Discrete Design Variables

Abstract

A method is presented for optimum design of structures, where some or all design variables can be chosen from a set of prescribed values. The main idea is to reduce the number of structural analyses in the process of optimization. First the structural responses such as forces and displacements are approximated as functions of cross-sectional properties, thus high quality explicit functions are generated for the responses. Employing these approximate expressions in the optimization process, the continuous optimum design can be achieved rapidly. Using the results obtained from the continuous variable optimization and with the help of the approximated responses, a branch and bound method is used to obtain the discrete design values. The results indicate that after the completion of the continuous variable optimization, only one or two extra detailed analyses of the structure is needed to complete the discrete variable optimization. In this work, a dome and a grillage are presented as test cases.