Comparative studies between Semi-analytical and shear deformation theories for functionally graded beam under bending

Abstract

In this paper, the bending response of functionally graded (FG) beam using three different approaches. viz. semi-analytical, higher-order shear and normal deformation theory (HOSNT), and trigonometric shear deformation theory (TSDT) under transverse loading conditions has been investigated. The boundary value problem (BVP) of the HOSNT and TSDT is derived using principle of virtual work whereas semi-analytical approach consist of formation of two-point BVP along the beam depth. All three models satisfy zero shear stress conditions at the top and bottom surfaces of the beam. The material properties of the FG beam vary across the thickness direction according to the power-law distribution. Aluminium-zirconia and aluminium-alumina are two types of compositions used to create FG beams. For comparison purpose, the authors have generated results for semi-analytical and HOSNT, being not available in the published literature. The numerical results are compared with previously published solutions to assess the correctness and effectiveness of the three models.

Keywords

• Functionally graded beam
• Shear deformation theory
• Semi-analytical
• Power-law