OPTIMUM DESIGN OF TRUSSES WITH DISCRETE SIZING AND SHAPE VARIABLES

The objective here is to present a method for optimizing truss structu res with discrete design variables. The design variables are considere d 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 m ethod, the structural responses, such as forces and displacements are approximated in each design cycle. The approximation of responses is c arried 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 ach ieved, the solution of which does not require the detailed finite elem ent analysis of the structure in each sub-optimization iteration. Firs t it is assumed that all the design variables are continuous and a con tinuous variable optimization is performed. With the results of this s tep, the branch and bound method is employed on the same approximate p roblem to achieve a discrete solution. The numerical results indicate that the method is efficient and robust in terms of the required numbe r of structural analyses. Several examples are presented to show the e fficiency of the method.