Evaluate the performance of an accelerated initial stiffness method in three dimensional finite element analysis

Abstract Newton’s method is a commonly used algorithm for elasto-plastic finite element analysis and has three common variations: the full Newton–Raphson method, the modified Newton–Raphson method and the initial stiffness method. The Newton–Raphson methods can converge to the solution in a small number of iterations when the system is stable; however, the methods can be quite computationally expensive in some types of problems, for example where the tangent stiffness matrix is unsymmetric or the plasticity is highly localized. The initial stiffness method is robust in those cases but requires a larger number of iterations. This prompted the formulation of many acceleration techniques in literature. In this paper, those techniques will be briefly discussed. This will be followed by the development of a modified acceleration technique for the initial stiffness method. The performance of the modified accelerated initial stiffness method will be examined in elasto-plastic analyses, using both direct and iterative matrix solvers. The results will be compared – in terms of the required number of iterations and the computation time – with an existing accelerated initial stiffness method, the non-accelerated initial stiffness method and the Newton–Raphson tangent stiffness method.