A Simple Numerical Solution Procedure for Equations of Nonlinear Finite Element Method

Abstract

The conventional solution strategy for nonlinear FEM of structural analysis is usually based on Newton-Raphson iteration under an additional constraint equation. So far a lot of nonlinear finite element solution procedures have been devised to provide the basis for most nonlinear finite element computer programs. In order to produce effective, robust solution algorithms, additional constraint equations for nonlinear FEM calculations in the load-displacement space of has been extensively investigated for the last a few decades. However, it is widely believed that due to the additional computations in the controlling of steps and directions of the iteration procedure, there will be more round-off errors accumulated to influence the convergence of solution. In this work, a more simplified solution procedure is presented, which is featured to be with neither iterations nor constraints. A Fortran computer program of the algorithm presented has been implemented in combining with a space truss element of co-rotational procedure. Verification of the procedure has been done by numerical example and a good result achieved.