Optimum design of trusses with discrete sizing and shape variables

Abstract

The objective here is to present a method for optimizing truss structures with discrete design variables. The design variables are considered to be sizing variables as well as coordinates of joints. Both types of variables can be discrete simultaneously. Mixed continuous-discrete variables can also be considered. To increase the efficiency of the method, the structural responses, such as forces and displacements are approximated in each design cycle. The approximation of responses is carried out with respect to the design variables or their reciprocals. By substituting these approximate functions of the responses into the original design problem, an explicit high quality approximation is achieved, the solution of which does not require the detailed finite element analysis of the structure in each sub-optimization iteration. First it is assumed that all the design variables are continuous and a continuous variable optimization is performed. With the results of this step, the branch and bound method is employed on the same approximate problem to achieve a discrete solution. The numerical results indicate that the method is efficient and robust in terms of the required number of structural analyses. Several examples are presented to show the efficiency of the method.