Buckling analysis of ۲D functionally graded porous beams using novel higher order theory

Functionally graded material is an in-homogeneous composite, constructed from various phases of material elements, often ceramic and metal and is employed in high-temperature applications. Aim of this work is to examine the behaviour of buckling in porous Functionally Graded Material Beams (FGBs) in ۲ directions (۲D) with help of fifth order shear deformation theory. With help of potential energy principle and Reddy’s beam theory, equilibrium equations for linear buckling were derived. Boundary conditions such as simply supported – Simply supported (SS), Clamped – clamped (CC) and Clamped-Free (CF) were employed. An unique shear shape function was derived and ۵th order theory was adapted to take into account the effect of transverse shear deformation to get the zero shear stress conditions at top and bottom surfaces of the beam. Based on power law, FGB material properties were changed in length and thickness directions. The displacement functions in axial directions were articulated in algebraic polynomials, including admissible functions which were used to fulfil different boundary conditions. Convergence and verification were performed on computed results with results of previous studies. It was found that the results obtained using ۵th order theory were in agreement and allows for better buckling analysis for porous material.

Keywords:

Buckling Behaviour , Fifth Order Shear Deformation Theory , Lagrange’s equations , ۲D FGB