Moving Element Method in the Dynamic Analysis of Functionally Graded Material Plates Subjected to Thermal Loads and Resting on a Variable Stiffness Foundation

This paper presents the development of a Moving Element Method (MEM) for analyzing the dynamic behavior of a functionally graded material (FGM) plate. The FGM plate is resting on a Pasternak foundation characterized by variable foundation parameters following a power-law distribution along the length of the FGM plate. Additionally, the plate is subjected to both thermal and moving loads. The governing equation of motion for the considered FGM plate is derived by applying the principle of virtual work. The determination of the total strains of the plate encompasses both temperature-induced strain and mechanical strain, achieved by employing the superposition principle. The governing equation of motion is discretized using the moving plate elements and subsequently assembled to generate the final system of equations. This system is then solved using the Newmark’s β numerical method. Prior to conducting the dynamic analysis of the FGM plates, accounting for the variable foundation parameters, two scenarios are investigated to verify the accuracy of the proposed model in comparison to previous studies. The findings of this study suggest that the elastic stiffness coefficient kwf exerts a notable influence on the displacement of the FGM plates, while the damping coefficient cf has a negligible impact on the plates’ behavior under the specified temperature conditions.