Flexural behavior of porous functionally graded plates using a novel higher order theory

In this paper, the flexural response of functionally graded plates with porosities is investigated using a novel higher order shear deformation theory, which considers the influence of thickness stretching. This theory fulfills the nullity conditions at the top and bottom of the plate for the transverse shear stresses, thus avoids the need of a shear correction factor. The effective material properties are computed through the rule of mixtures. The principle of virtual displacements is employed to derive the equilibrium equations. The Navier’s method is adopted to obtain the solutions in closed form for simply supported boundary conditions. The accuracy and consistency of the developed theory are established with numerical results of perfect and porous functionally graded plates available in the open literature. The dimensionless transverse displacements and stresses have been reported. The effect of even, uneven and logarithmically-uneven porosity distributions with different porosity volume fraction, gradation index, side-to thickness ratios and aspect ratios are studied. The numerical results show that, the increase of volume fraction of porosity increases the dimensionless transverse deflections and axial stresses, and decreases the transverse shear stresses. No variation of transverse shear stresses observed for a completely ceramic and metallic plate for all kinds of porosity models. The provided numerical results can be used to evaluate various plate theories and also to compare the results of other analytical methods and finite element methods.