Preconditioned improved bi-conjugate gradient in nonlinear analysis of space trusses

Different methods for analyzing nonlinear systems have been proposed. Most of them are not fast enough and also fail to deal with particular set of equations like nonlinear analysis of structures. In this paper, the preconditioned biconjugate gradient (PBCG) is combined with the Newton-Raphson method to reduce the convergence time of each iteration in nonlinear solution process. This algorithm replaces the procedure of inversing the tangent stiffness matrix with a new iterative method to solve the linearized system of equations. Also a new method is introduced to reduce computational time by applying preconditioning to the improved biconjugate gradient method. The proposed method is useful to analyze complex behavior structures, including unloading, snap-through buckling, and inelastic post-buckling analyses. In this paper a new preconditioner is proposed which is suitable for nonlinear analysis of structures. Results show that using the new methodology maintains the accuracy in an acceptable level while reduces computational cost and time, significantly.