Geometrically Nonlinear Finite Element Analysis of Cantilever Beams Using MATLAB

Abstract

In this research, a Total Lagrangian Formulation for Geometric Nonlinear Beams problems based on green strains was developed. Geometric Nonlinear Total Lagrangian formulations applied on two-dimensional beam finite elements were used. The formulations were implemented by using MATLAB program. The solution of linear and nonlinear equations was obtained by the Incremental method. The program was applied to obtain the displacements, reactions and stress resultants resulting from incremental strains. The accuracy of the results was checked by using two numerical examples. The linear results are in close agreement with known results. Acceptable nonlinear results are obtained for pure incremental solutions only. Incremental iterative solutions are obtained for some specific cases only.