A four node quadrilateral shell element for free vibration response of functionally graded spherical shell panels under thermal environment

The current work involves the free vibration analysis of the FG spherical shells under the thermal conditions using four node quadrilateral shell element. This four-node shell element has 7 DOF per node, which include 3 displacements, 2 rotations, and 2 transverse shear strain components. The authors developed the four node quadrilateral shell element by modifying the discrete Kirchhoff quadrilateral shell element based on Reddy's third-order theory that they previously developed for the cylindrical shell. In the present work functionally graded spherical shell panels with simply supported as well as clamped boundary condition, with various radius to span ratios and with different volume fraction subjected to nonlinear temperature rise, are analysed. The material property variation is considered as per Mori- Tanaka method in the present study. The results are compared with the results obtained using Ansys to evaluate the performance of the developed element. Comparison of results shows that the developed element gives quite perfect results even with the coarser mesh, which indicates the high efficiency of present element.