Reliability-Based Optimal Design of Truss Structures Using Particle Swarm Optimization

Abstract

In this work, the particle swarm optimization method is employed for the reliability-based optimal design of statically determinate truss structures. Particle swarm optimization is inspired by the social behavior of flocks (swarms) of birds and insects (particles). Every particle's position represents a specific design. The algorithm searches the design space by adjusting the trajectories of the particles that comprise the swarm. These particles are attracted toward the positions of both their personal best solution and the best solution of the swarm in a stochastic manner. In typical structural optimization problems, safety is dealt with in a yes/no manner fulfilling the set of requirements imposed by codes of practice. Considering uncertainty for the problem parameters offers a measure to quantify safety. This measure provides a rational basis for the estimation of the reliability of the components and of the entire system. Incorporating the reliability into the structural optimization framework one can seek a reliability-based optimal design. For the problems examined herein, the reliability indexes of the structural elements are obtained from analytical expressions. The structure is subsequently analyzed as a series system of correlated elements and the Ditlevsen bounds are used for the calculation of its reliability index. The uncertain-random parameters considered in this work are the load, the yield-critical stress; and the cross sections of the elements. The considered design variables of the optimization problem are the cross-sectional areas of the groups, which control the size of the truss, and the heights and lengths that control the shape of the truss. The results of the optimization are presented for a 25-bar truss and a 30-bar arch and the robustness of the optimization scheme is discussed.