Issue 51

S. Merdaci et alii, Frattura ed Integrità Strutturale, 51 (2020) 199-214; DOI: 10.3221/IGF-ESIS.51.16 200 appropriate design. Frequently, FG plates are made from a mixture of two phases (metallic and ceramic) in which volume fraction of phases changing through the thickness. To remedy such defects, functionally graded materials (FGMs), within which material properties vary continuously, have been proposed. The concept of FGM was proposed in 1984 by a group of materials scientists, in Sendai, Japan, for thermal barriers or heat shielding properties [1]. Functionally graded materials (FGMs) are recently developed advanced composite materials and are being widely used in various engineering appliances such as nuclear reactors and high speed spacecraft industries. In recent years, these materials have found other applications in electrical appliances, energy transformation, biomedical engineering, optics, etc. [2]. However, in the manufacture of FGM, porosities may occur in the materials during the sintering process. This is due to the large difference in coagulation temperature between the components of the material [3]. Wattanasakulpong et al. [4] discussed the porosities that occur in lateral FGM samples made with a multistage sequential filtration technique. So, it is important to take under consideration the porosity effect when designing FG components under the effect of dynamic loadings. Based on the open literature, it seems that many investigators have paid attention to the analysis of FGM structures with porosities. Most of these investigations are concerned with the vibration behavior of FG porous structures [5–19]. The objective of this article is to present the static of bending behavior of sandwich plates FGM having porosities. The sandwich plate may be either perfectly porous homogeneous or has a perfect homogeneity shape depending on the values of the volume fraction of voids (porosity) or of the graded factors. The sandwich plate is assumed isotropic at any point within the plate, with its Young’s modulus varying across its thickness in accord with a power law P-FGM in terms of the volume fractions of the sandwich plate constituents while the Poisson’s ratio remains constant. The present theory satisfies equilibrium conditions at the sandwich plate’s top and bottom faces without using shear correction factors. A Navier’s solution is used to obtain closed-form solutions for simply supported sandwich plates FG symmetrical. Several important aspects, i.e. aspect ratios, thickness ratios, exponent graded factor as well as porosity volume fraction, which affect deflections and stresses, are investigated. This paper explores the following elements:  Formulation of the problem (Structural model and Displacement field and constitutive equations)  Equilibrium equations  Analytical solutions for FGM sandwich plate  Numerical results and discussions F ORMULATION OF THE PROBLEM Structural model onsider a FG thick rectangular plate of length a, width b and thickness h made of functionally graded material as shown in Fig.1 together with the adopted coordinate system. The material properties of the FG plate, such as Young’s modulus E, are assumed to be function of the volume fraction of constituent materials. Figure 1: Geometry and coordinates of the porous sandwich plate FGM. Let the sandwich plate FGM be subjected to a transverse load q(x, y) , and a rectangular Cartesian coordinate of x and y is introduced for the deformation analysis of the plate. The plate under study is bounded by the co-ordinate planes 0 ≤x ≤ a and 0 ≤y ≤ b. The reference surface is the middle surface of the plate defined by z =0, and z denotes the thickness co- ordinate measured from the un-deformed middle surface. C