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Journal of Applied Mathematics
Volume 2014, Article ID 932314, 12 pages
http://dx.doi.org/10.1155/2014/932314
Research Article

Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method

1Department of Computer Engineering, Bilkent University, 06800 Ankara, Turkey
2Department of Mechanical Engineering, Bilkent University, 06800 Ankara, Turkey

Received 29 May 2014; Revised 24 July 2014; Accepted 6 August 2014; Published 28 August 2014

Academic Editor: Henggui Zhang

Copyright © 2014 Emir Gülümser et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.