A robust and efficient iterative strategy for nonlinear analysis of structures subjected to buckling

The paper shows how to make the incremental-iterative solution significantly more efficient and robust in geometrically non-linear structural problems discretized via displacement-based finite element formulations. The main idea is to relax the constitutive equations at each integration point (IP) during the iterations. The converged solution remains unchanged while the iteration matrix is computed using independent IP stresses. This reduces the number of iterations to obtain convergence and allows very large steps in incremental analyses. The computational cost of each iteration is the same as the original Newton method. Importantly, the robustness of the iterative process is unaffected by high membraneto-flexural stiffness ratios as opposite to the standard Newton method.