A Smooth Gradation Based FE Model for Dynamic Analysis of Functionally Graded Plates and Folded Plates in Hygrothermal Environments

Abstract

Functionally graded (FG) plates and folded plates are now integral components in aerospace, aviation, nuclear, and marine structures. Modelling FG structures with diverse material properties presents notable challenges, often necessitating the use of custom coding and analytical methods which may not always be suitable for commercial projects due to their time-consuming nature. It is from this perspective that a novel computational model based on the finite element (FE) approach is developed in the present research for free vibration analysis of FG plates and folded plates under hygrothermal conditions. A smooth gradation based material modelling is implemented in the FE model for FG structures using an analytical function, adhering to the power law, within the COMSOL Multiphysics software. The first order shear deformation theory is implemented to model the FG plate. Both the linear and uniform rise of temperature through the plate's thickness are considered whereas the moisture concentration is assumed to rise uniformly. The prestressed eigenfrequency analysis is adopted so that the residual stresses resulting from non-linear strains generated due to hygrothermal effect can be incorporated. The results of the present FE model are validated with other analytical methods and the layerwise theory based approach from published literature. Thorough numerical simulations involving variations in temperature, moisture, power law indices, crank angle, boundary conditions and thicknesses are conducted to explore the vibrational behavior of the FG panels in hygrothermal conditions. The presented computational model offers an efficient and straightforward approach for the dynamic analysis of FG panels having complex geometries and boundary conditions in extreme environments.