Analysis of Geometrically Nonlinear Euler-Bernoulli Beam using EFGM

Abstract

The current paper presents a meshless formulation for the analysis of geometrically nonlinear one-dimensional Euler-Bernoulli beams. Element-free Galerkin method (EFGM) is used as the meshless numerical tool and Newton-Raphson method as the iterative scheme. Numerical examples of beams with four different boundary conditions are solved, and the results are compared with that of the finite element method (FEM). EFGM results are found in good agreement with that of FEM. Also, it is found that EFGM eliminates the effect of membrane locking in thin beams.