Effect of elastic foundation and porosity on buckling response of linearly varying functionally graded material plate

This work presents the buckling response of porous plate made of functionally graded materials (FGMs). A tapered FGM plate with uniaxial and biaxial loading under numerous boundary conditions was investigated. Simple power law and sigmoidal law are applied to compute the tailored material properties. Further, the effect of Pasternak foundation on the buckling response for a plate is computed, considering the five types of porosity pattern. The first order-shear deformation theory (FSDT) is used to describe the kinematic field of the plate. The variational principle is used to derive the equation of motions. Subsequently, the solution for buckling analysis is found by applying the Galerkin's-Vlasov method. It has been seen that the effect of elastic foundation largely influenced the buckling response of FGM plate, especially Pasternak foundation has significant effect when comparing with Winkler's foundation. Similarly, buckling load, subjected to uniaxial or biaxial compression of plate, decreases greatly for porous material. Numerical examples for computing buckling response are compared for accuracy and verification purpose of the present formulation, with earlier published results. Considering the effect of thickness variation, span ratio, compressive load conditions, foundation stiffness and porosity on buckling analysis are estimated and established as a benchmark result in tabulated form. Moreover, parametric studies have been done, by keeping in view, to explore the utility of FGM tapered plate and the responses represented in the graphically form.