Demonstration of a simple method to satisfy homogenous boundary conditions in element-free Galerkin method through the vibration problem of Timoshenko beam

Abstract

A simple method to satisfy the homogeneous boundary condition in the element-free Galerkin method is proposed in this paper. Effectiveness of the method is demonstrated, through free vibration problems of Timoshenko beams. Several case studies involving different slenderness ratios and end conditions are carried out. The results of the present study are compared with those obtained using classical Rayleigh-Ritz and conventional element-free Galerkin method wherein Lagrangian multipliers are employed to satisfy boundary conditions. Eventhough, a one-dimensional problem is considered in the present paper, the validity of the proposed method for the two-dimensional problems is demonstrated theoretically.