Elastodynamics of FGM plates by mesh-free method

Abstract

The paper deals with transient analysis of homogeneous as well as FGM (functionally graded material) thin and/or thick plates subjected to transversal dynamic loading. The Young modulus and mass density are allowed to be continuously variable through the thickness of the plate. The unified formulation is developed for plate bending problems including three various theories such as the classical Kirchhoff–Love theory for bending of thin elastic plates, the 1st and 3rd order shear deformations plate theories. Switching among these three theories is controlled by two key factors. From the derived equations of motion, the coupling between the bending and in-plane deformation modes is discovered in FGM plates with specification of the necessary conditions. For the numerical implementation, the strong formulation is proposed with meshless approximation of spatial variations of field variables. The semi-discretized equations of motion yield a system the ordinary differential equations which can be solved by standard time stepping techniques. The great attention is paid to the numerical study of coupling effects in FGM plates subjected to transversal Heaviside impact loading and/or Heaviside pulse loading. The achieved numerical results are thoroughly discussed and interpreted.