Investigation of Static Behaviour of Rectangular Isotropic Porous Plate with Different Boundary Conditions

This article investigates the static behaviour of a rectangular isotropic plate having two different types of porosity, namely even porosity and uneven porosity. The plate is subjected to different combinations of mixed edge constraints, viz. simply supported, clamped, and free. The behaviour of static parameters (α, β, and β′) associated with bending and normal stresses has been studied for the plate under different loading conditions, namely uniformly distributed load (UDL), and sinusoidal load (SL). Classical plate theory (CPT) has been used during the course of analysing the static bending of the plate and the governing differential equations have been derived by using the energy principle. The Rayleigh–Ritz method with an algebraic polynomial has been used to solve those governing differential equations. This mathematical formulation presents simple, accurate, and computationally quick numerical results. The convergence of static parameters has been obtained by increasing the number of polynomials of the displacement function. To validate the proposed model, the static parameters calculated by the current technique are first compared to the available literature. The effect of aspect ratios and porosity volume fraction on static parameters has been comprehensively explored for different boundary conditions. Numerical values of static parameters are higher for porous rectangular plate than that of nonporous rectangular plate. The effect of aspect ratios on the static parameters of porous rectangular plates has also been examined. As the aspect ratio raises, the value of static parameters also increases because the plate becomes less stiff as the aspect ratio increases. It is also observed that the free edge constraints have higher value of static parameters, whereas clamped edge constraints have the least. The results obtained from this study can be used for future reference.