Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element

This paper formulates an efficient third-order shear deformation beam element for free vibration and buckling analysis of bidirectional functionally graded sandwich (BFGSW) beams. The beams consist of three layers, an axially functionally graded core and two face sheets with material properties varying in both the thickness and length directions by power-law distributions. The element is derived in this paper for the first time by using hierarchical functions to enrich the Lagrange and Hermite interpolations of a conventional beam element, and this enrichment results in a super convergent beam element. Using the formulated beam element, natural frequencies and buckling loads are evaluated for the beams with various boundary conditions. The effects of the material distribution and the layer thickness on the vibration and buckling characteristics are examined in detail and highlighted. The influence of the micromechanical models, namely the Voigt model and Mori-Tanaka scheme used in estimating the effective material properties, on the vibration frequencies and buckling loads of the beams is also examined and discussed. © 2020