A material-based higher-order shear beam model for accurate analyses of FG beams with arbitrary material distribution

Abstract

A material-based higher-order shear beam model is proposed for accurate analyses of functionally graded (FG) beams with arbitrary material distribution through thickness. Distinct from the existing higher-order shear beam models, the shear function of the present model is dependent on the material distribution. The specific form of this material-based shear function is described by a piecewise linear interpolation field and determined by ensuring the consistency of transverse shear stress distributions between Euler-Bernoulli beam theory and the higher-order shear beam theory. Based on the proposed beam model, a 3-node beam finite element is developed for static and buckling analyses. Numerical examples are studied to visualize the accuracy and effectiveness of the proposed model and finite element. Solutions of static displacements and critical loads obtained by various beam elements including the proposed element, the existing displacement-based beam elements and the mixed higher-order shear beam element are compared. The accuracy loss of the existing higher-order shear beam models is discussed. As demonstrated by the results, the proposed beam model and finite element have excellent solution accuracy and desirable applicability.