Framework for Finite-Element–Based Large Increment Method for Nonlinear Structural Problems

This paper addresses the formulation and application of a finite-element–based large increment method for solving nonlinear structural problems. In a step-by-step solution of a nonlinear problem based on the displacement method, the main unknown variables are the system displacements. Therefore, to represent the general force in terms of general deformation, the constitutive relations have to be linearized. As such, a step-by-step incremental procedure is often used, where the solution at the current step is added to the solution of the previous step, thereby, successive steps are eventually used to achieve a solution. However, a flexibility-based large increment method can be useful to solve nonlinear problems if linearization of the constitutive relationship can be avoided. This paper presents a novel methodology based on the flexibility method to solve nonlinear problems with a large increment methodology. The idea is built on using a nonlinear material model without the need for linearization and a step-by-step approach. In doing so, the mathematical background, governing equations, solution methodology, and framework to implement the method on a parallel computation platform are presented in detail. The methodology has been demonstrated using a simple nonlinear problem. The demonstration example clearly reveals the accuracy and the efficiency of the method.