Nonlinear Dynamic Response of a Temperature-Dependent FGM Spherical Shell under Various Boundary Conditions and Thermal Shocks: Examination of Dynamic Snap-through

In this study, a comprehensive exploration of the nonlinear dynamic snap-through phenomenon observed in shallow spherical shells composed of functionally graded materials (FGMs) is examined. The analysis encompasses the interplay of thermomechanical characteristics within metal and ceramic phases, taking into account their temperature-dependent behaviors. To address this problem, the transient heat conduction equation in a nonlinear form, accounting for the temperature dependence factor is derived. To solve this complexity, the Generalized Differential Quadrature (GDQ) method is employed, coupled with the Crank-Nicolson time integrating scheme, leveraging an iterative approach for precision. The formulation of nonlinear dynamic motion equations is based on Hamilton's principle and incorporates the utilization of nonlinear strain-displacement equations and uncoupled thermoelasticity. In the spatial domain, GDQ proves invaluable in solving these nonlinear, coupled equations. In the temporal domain, the Newmark procedure in conjunction with the Newton-Raphson iterative method are utilized to navigate through dynamic equations, yielding insights into shell's behavior over time. In the initial stages of the investigation, we validate our spherical shell formulation and methodologies by comparing shell's response with existing, simpler works. This step ensures the reliability and accuracy of our model. The primary objective is to assess the presence and characteristics of the thermal snap-through phenomenon within the shell under these diverse conditions.