Modeling and static analysis of porous functionally graded and FG-sandwich plates

The present work is emphasized towards the development of models for the porosity occurring in the functionally graded (FG) structures. The porosities are modeled across the thickness for the FG plate as well as for the FG core of the sandwich plate considering three different types of porosity distribution i.e. symmetric center enhanced, top enhanced, and bottom enhanced. The influence of the porosities on the material properties is examined and the properties are evaluated in the presence of porosities. Further, the influence of the porosities on the static behavior of FG and FG-sandwich plates is investigated quantitatively wherein the considered structures are modeled in the framework of an inverse hyperbolic shear deformation theory. The governing equations are obtained through principle of virtual work considering linear structural kinematics and generalized Hooke's law. These equations are solved in the closed form for the simply supported boundary conditions and the response is obtained. The results are verified with the existing literature wherever possible and are in good agreement. The effect of various parameters such as porosity distribution, porosity parameter, core-thickness distribution, span-thickness ratio, power-law index, and loading conditions on the static response is examined and, on those basis, noteworthy conclusions are made. The results indicate that the plate with top enhanced porosity distribution possess lowest deflection while the plate with bottom enhanced distribution possess the highest deflection.