Optimal design program for truss and beam structure using a generalized steepest descent method

Abstract

A computer program for optimal structural design has been developed based on a generalized steepest descent algorithm. The program can handle structures with truss and/or beam elements. The design criterion used is to minimize the structural weight. Constraints on stress level, nodal displacements, and natural frequency as well as on design variables are imposed. The design variables include more than one geometric variable of each cross section of the structural element. To accomodate certain symmetry of a structure, design variable linking, where same design value is taken for several members, has been incroporated. Matrix structural analysis is used for the structural analysis part in the program. For the calculation of natural frequency and fundamental mode, subspace iteration method is utilized. Detailed description on the method of analysis and optimization is given along with several example solutions, including a space truss design, a plane frame and a Darrieus type vertical axis wind turbine design. The results are compared with existing literature available.