A finite element formulation for thermally induced vibrations of functionally graded material sandwich plates and shell panels

A finite element formulation based on a higher-order layerwise theory is presented for the first time to investigate thermally induced vibrations of functionally graded material (FGM) sandwich plates and shell panels. The properties of FGM sandwich are assumed to be position and temperature dependent. The upper and lower layers of the sandwich panel are considered to be made of pure ceramic and metal, respectively and the elastic properties of FGM core are varied according to a power-law function. The top surface is exposed to a thermal shock and the bottom surface of the panel is either kept at a reference temperature or thermally insulated. The one-dimensional transient heat conduction equation is solved using a central difference scheme in conjunction with the Crank-Nicolson method. A higher-order layerwise theory is used for FGM sandwich panels, in which a higher-order displacement field for the FGM core and a first-order displacement field for the facesheets are assumed. The governing equations are solved using Newmark average acceleration method. It is shown that the proposed layerwise finite element formulation is simple and can easily be applied to investigate FGM sandwich plates and shell panels subjected to rapid heating.