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.

A Nonlinear Beam Finite Element with Bending–Torsion Coupling Formulation for Dynamic Analysis with Geometric Nonlinearities

“…Other models for static and dynamic nonlinear analysis of beam structures exist in the literature and employ different solutions to simulate specific conditions. Some models consider only one-dimensional finite elements as in [13], while other developed models consider all the possible degrees of freedom. Yang et al [14] developed a six degree of freedom beam element, including material nonlinearity; they described a procedure for nonlinear static analysis which involves piecewise linearization of the response equations and iterations at each incremental step to achieve equilibrium.…”