Free vibration response of cylindrical and spherical functionally graded material shell panels using a quadrilateral finite element

Abstract

A quadrilateral element is developed for analysing the free vibration responses of moderately thick spherical and cylindrical FGM shell panels. The element has seven degrees of freedom per node namely, two transverse shear strain components, two bending rotations, two in-plane, and one transverse deflections. The transformation matrix is developed by using two separate co-ordinate systems namely: Cartesian and Surface, to convert the actions and displacements from global to local directions and vice versa. The local degrees of freedom related to displacements are transformed to a Cartesian coordinates system (x, y, z). The degrees of freedoms which are related to rotations are transformed to surface-coordinate system (ξ1, ξ2, ξ3), in which ξ3 is taken normal to the shell surface at every node of the element. The material property variation through the thickness is considered accordingly Mori-Tanaka scheme. The results for cylindrical and spherical shell panels having different geometrical configurations, volume fraction configurations and different boundary conditions are compared with the available 2D analytical and 2D finite elements results available in the literature. For some cases, the present results of non-dimentionalised frequencies are compared with those obtained using ANSYS (APDL). It is observed that the performance of the numerical evaluation with the present element (DKTOTS-FG) is quite satisfactory for free vibration response of functionally graded material spherical and cylindrical shells in this study.