Nonlinear transient response of functionally graded shallow spherical shells subjected to mechanical load and unsteady temperature field

This paper is concerned with the transient deformation of functionally graded (FG) shallow spherical shells subjected to time-dependent thermomechanical load. Based on Timoshenko-Mindlin hypothesis and von Karman nonlinear theory, a set of nonlinear governing equations of motion for FG shallow spherical shells in regard to transverse shear deformation and all the inertia terms are established using Hamiltonʹs principle. The collocation point method and Newmark-beta scheme in conjunction with the finite difference method are adopted to solve the governing equations of motion and the unsteady heat conduction equation numerically. In the numerical examples, the transient deflection and stresses of FG shallow spherical shells with various material properties under different loading conditions are presented.