This paper addresses the formulation and application of a finite-element-ba
sed large increment method for solving nonlinear structural problems. In a
step-by-step solution of a nonlinear problem based on the displacement meth
od, the main unknown variables are the system displacements. Therefore, to
represent the general force in terms of general deformation, the constituti
ve relations have to be linearized. As such, a step-by-step incremental pro
cedure is often used, where the solution at the current step is added to th
e solution of the previous step, thereby, successive steps are eventuality
used to achieve a solution. However, a flexibility-based large increment me
thod can be useful to solve nonlinear problems if linearization of the cons
titutive relationship can be avoided. This paper presents;a novel methodolo
gy based on the flexibility method to solve nonlinear problems with a large
increment methodology. The idea is built on using a nonlinear material mod
el 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 simp
le nonlinear problem. The demonstration example clearly reveals the accurac
y and the efficiency of the method.