A stress approach model for elastodynamic problems of functionally graded plates

Abstract

This paper aims to develop the first stress approach model for elastodynamic problems of functionally graded plates. The new model is called SAM-FG7, and like many other plate models, it is an alternative to solid finite elements to avoid high computational cost calculations for thickness ratios ranging from moderately thick to thin. SAM-FG7 stress approximation is intended to improve the stress results of models based on a displacement approach; the approximation is also an enhancement of that of the static shell model SAM-FG applied to plates since it considers two additional generalized forces. In statics, the SAM-FG7 stress field verifies the 3D equilibrium conditions, and the generalized equations are obtained by using the minimum complementary energy principle. For dynamic problems, a consistent derivation of the generalized motion equations is obtained by applying the method proposed by Bouteiller et al. (2022). SAM-FG7 features seven generalized displacements, i.e., two more fields than SAM-FG. Its equations were implemented and solved in COMSOL Multiphysics 6.2 finite element software. To validate the model, eigenfrequencies and modal stresses for a family of square functionally graded plates are calculated and compared with those given by solid finite elements and other models found in the literature. In order to demonstrate the accuracy of the model in more complicated problems, perforated functionally graded plates with transversely isotropic materials are considered; free vibration and frequency response analyses are made. SAM-FG7 predictions accurately approximate solid finite element results.