Practical design optimization of truss structures using the genetic algorithms

Abstract

Truss structures are widely employed in the industrialized world. They appear as bridges, towers, pylons, roof supports, building exoskeletons or high technology light space structures. This paper investigates the simultaneous size, geometry and topology optimization of real life large truss structures using genetic algorithms (GAs) as optimizer and finite element method as analyzer. In general, the large truss structures are constructed for practical reasons from the duplication of some basic structures called bays. Thus, the final optimum design may be reached by optimizing the characteristics of the basic bays instead of optimizing the whole structure. Both single and multiobjective functions based on the mass of the structure and the maximum nodal displacement have been considered as the cost functions. In order to obtain realistic optimal designs, the cross-sectional areas have been extracted from the standard profiles according to AISC codes and practical conditions are imposed on the bays. The design optimization problem is also constrained by the maximum stress, maximum slenderness ratio and the maximum and minimum cross-sectional area of the truss members. To accommodate all these constraints, two different penalty functions are considered. The first penalty function considers the normalization of violated constraints with respect to the allowable stress or slenderness ratio. The second penalty function is a constant function which is used to penalize the violations of the slenderness ratio. Three illustrative examples of realistic planar and space truss structures have been optimized to demonstrate the effectiveness of the proposed methodology. However, other criteria such as cost and/or manufacturability could be quantified and included in the optimization formulation.