Analysis of Stability and Oscillations of Porous Power and Sigmoid Functionally Graded Sandwich Plates by the R-Function Method

Abstract

In this paper, the R-function method is used for the first time to study the stability and oscillations of porous functionally graded (FG) sandwich plates with a complex geometric shape. It is assumed that the outer layers of the plate are made of functionally graded materials (FGM), and the filler is isotropic, namely ceramic. The differential equations of motion were obtained using the usual first-order shear deformation theory with a given shear coefficient (FSDT). Two models of porosity distribution according to the power (P-law) and sigmoid (S-law) laws were studied. Analytical expressions for calculating the effective mechanical characteristics of FG materials with even and uneven porosity distribution were obtained. The proposed approach takes into account the fact that the subcritical state of the plate can be heterogeneous, and therefore, first of all, the stresses in the middle plane of the plate are determined, and then the eigenvalue problem is solved in order to find the critical load. To determine the critical load and plate frequencies, the Ritz method was used along with the R-function method. The developed algorithms and software are tested on test examples and compared with known results obtained using other methods. A number of problems of stability and oscillations of the FG of porous sandwich plates with a complex geometric shape for various layer stacking schemes, various boundary conditions and laws of porosity distribution have been solved.