Simulations of Coupling Effects in Vibration of FGM Plates by Mesh-Free Methods - Sladek, V.; Sator, L.; Sladek, J. (International journal of computational methods and experimental measurements, 2017)
In this paper, we present briefly the derivation of the equations of motion and boundary conditions for elastic plates with functionally graded Young’s modulus and mass density of the plate subjected to transversal transient dynamic loads. The unified formulation is derived for three plate bending theories, such as the Kirchhoff–Love theory (KLT) for bending of thin elastic plates and the shear deformation plate theories (the first order – FSDPT, and the third order – TSDPT). It is shown that the transversal gradation of Young’s modulus gives rise to coupling between the bending and in-plane deformation modes in plates subject to transversal loading even in static problems. In dynamic problems, there are also the inertial coupling terms. The influence of the gradation of material coef- ficients on bending and in-plane deformation modes with including coupling is studied in numerical experiments with consideration of Heaviside impact loading as well as Heaviside pulse loading. To decrease the order of the derivatives in the coupled PDE with variable coefficients, the decomposition technique is employed. The element-free strong formulation with using meshless approximations for spatial variation of field variables is developed and the discretized ordinary differential equations with respect to time variable are solved by using time stepping techniques. The attention is paid to the stability of numerical solutions. Several numerical results are presented for illustration of the coupling effects in bending of elastic FGM (Functionally Graded Material) plates. The role of the thickness and shear deformations is studied via numerical simulations by comparison of the plate response in three plate bending theories.