An extension of Carrera unified formulation in polar coordinate for analysis of circular sandwich plate with FGM core using GDQ method

Abstract

The Carrera Unified Formulation (CUF) is a technique that, in addition to eliminate the imperfections of other theories, allows us to achieve a large class of models, such as equivalent single layer, layer wise, and mixed formulation in a unified manner. For this reason, this formulation can be very effective in different analyses, and according to the desired analysis, an appropriate model could be chosen. In this research, for the first time, the Carrera Unified Formulation is extended in the polar coordinates for analyzing the sandwich circular plate with the functionally graded material core. In order to apply variations in the properties of the functionally graded material, the variable kinematic method is used in the frame work of CUF, which ultimately leads to a reduction in degrees of freedom and an increase in the accuracy of the results. The functionally graded material is modeled as a mixture of ceramics and metal, whose properties change according to a power distribution in the direction of thickness. In this research, the generalized differential quadrature (GDQ) method is used to solve the governing equations. The obtained results are compared with the existing three-dimensional results as well as the generalized Zig-Zag theory, which indicates the high accuracy of the CUF formulation for circular plates in the polar coordinates. In addition, new results are provided for different geometries, thickness ratios, boundary conditions as well as deflection, radial displacements, annular and radial stresses, and transverse stresses along the thickness.