Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints

Abstract

The current manuscript develops a novel mathematical formulation to portray the static deflection of a bi-directional functionally graded (BDFG) porous plate resting on an elastic foundation. The correctness of the static response produced by middle surface (MS) vs. neutral surface (NS) formulations, and the position of the boundary conditions, are derived in detail. The relation between in-plane displacement field variables on NS and on MS are derived. Bi-directional gradation through the thickness and axial direction are described by the power function; however, the porosity is depicted by cosine function. The displacement field of a plate is controlled by four variables higher order shear deformation theory to satisfy the zero shear at upper and lower surfaces. Elastic foundation is described by the Winkler–Pasternak model. The equilibrium equations are derived by Hamilton’s principles and then solved numerically by being discretized by the differential quadrature method (DQM). The proposed model is confirmed with former published analyses. The numerical parametric studies discuss the effects of porosity type, porosity coefficient, elastic foundations variables, axial and transverse gradation indices, formulation with respect to MS and NS, and position of boundary conditions (BCs) on the static deflection and stresses.