A meshfree method for thermodynamic analysis of functionally graded elliptical shell with varying thickness in supersonic flow

This study presents a meshfree Jacobi-radial point interpolation (Jacobi-RPI) method for the dynamic analysis of functionally graded elliptical shell with varying thickness (FGESVT) in supersonic flow and thermal environment. The material properties of FGESVT are assumed to vary along the direction perpendicular to the bottom surface. The thermal stress due to the variation of environmental temperature is considered by introducing the nonlinear part of the Green–Lagrange strain. A meshfree shape function is constructed by combining the radial basis with Jacobi polynomials with fast convergence, numerical stability and high accuracy, and the displacement components of the FGESVT are expanded by using the meshfree Jacobi-RPI shape function. The equations of motion of the closed FGESVT are obtained by coupling the equations of several open shells. The accuracy and reliability of the proposed method are validated through a sufficient number of numerical studies for the free vibration and dynamic response analysis of open and closed FGESVT. Finally, the effect of thermal load, thickness variation and boundary condition on the free vibration and dynamic response of the FGESVT are discussed.