A new algorithm in nonlinear analysis of structures using particle swarm optimization

Solving systems of nonlinear equations is a difficult problem in numerical computation. Probably the best known and most widely used algorithm to solve a system of nonlinear equations is the Newton-Raphson method. A significant shortcoming of this method becomes apparent when attempting to solve problems with limit points. Once a fixed load is defined in the first step, there is no way to modify the load vector should a limit point occur within the increment. To overcome this defect, displacement control methods for passing limit points can be used. In the displacement control method, the load ratio in the first step of an increment is defined so that a particular key displacement component will change only by a prescribed amount. In this paper, the load ratio is obtained using a Particle Swarm Optimization (PSO) algorithm so that the complex behavior of structures can be followed, automatically. The design variable is load ratio, and its unbalanced force is also considered an objective function in the optimization process. Numerical results are performed under geometrical nonlinear analysis, elastic post-buckling analysis and inelastic post-buckling analysis. The efficiency and accuracy of proposed method are demonstrated by solving numerical examples