Free vibration and buckling analysis of axially functionally graded tapered Timoshenko beams using B-spline-based isogeometric analysis

Abstract

This study considers Timoshenko beam theory and the isogeometric analysis method to investigate the free vibration and buckling of axially functionally graded (AFG) tapered beams. The governing equations are obtained from the kinematic assumptions of Timoshenko beam theory and Hamilton's principle. The isogeometric analysis approach is implemented to solve the motion equations. One-dimensional B-spline basis functions are used to estimate the displacement field, describe the geometry, and illustrate the deformed shapes of the beam. Due to suffering the isogeometric approach from the shear locking phenomenon, the selectively reduced integration is applied. It is shown that this method can mitigate the effect of shear locking. In this attempt, the effect of material non-homogeneity parameters, mass density, Young's modulus, and taper ratio on the critical buckling loads and natural frequencies are considered for various boundary conditions. Several numerical examples show the accuracy and reliability of this method. The obtained results are in accord with the ones in the related articles and can be adopted as future reference solutions.

Keywords

• Buckling
• Free vibration
• Axially functionally graded material
• Isogeometric
• Tapered timoshenko beam