Elasto-plastic Analysis of Cantilever Beams, By The Meshless Local Petrov-Galerkin (MLPG)Method

In this paper a meshless method based on the local petrov-galerkin approach is proposed for the elastoplastic analysis of cantilever beams. Galerkin weakform formulation is applied to derive the discrete governing equations and integration is performed using gauss quadrature. A linear elastic analysis, using moving least square approximation function, is carried out for the determination of stress field of material nonlinear problems using material parameters as field variables. Hencky's total deformation theory is used to define effective elastic material parameters, which are treated as spatial field variables and considered as functions of the equilibrium stress state and material properties. These effective material parameters are obtained in an iterative process based on strain controlled projection method, using experimental uniaxial tension test curve. Numerical results obtained from present method are compared with those obtained from standard nonlinear finite element method and are found to be in good agreement.

Keywords:

MLPG Method , Elasto-plastic analysis , MLS approximation , Hencky's total deformation theory