A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams

This paper presents a simple two-variable shear deformation theory for bucking, bending, and vibration behaviours of functionally graded porous (FGP) beams. The displacement field of beams is developed from the separation of variables. Three typical porosity distribution types are considered. Mass density and elastic modulus of FGP beams are assumed to be graded in the beam’s thickness. Governing equations are derived from Lagrange’s principle. The exponential approximation functions are developed for various boundary conditions to predict frequency, buckling load, deflection, and stress of beams. The effects of boundary condition, span-to-height ratio, porous distribution pattern, porosity parameter, and shear deformation on the critical buckling load, frequency, deflection, and stress of beams are investigated in detail.