Geometrically Nonlinear Rapid Surface Heating in FGM Hermetic Capsule

The present study examines the geometrically non-linear dynamic response of hermetic capsule construction made of functionally graded materials subjected to thermal shock. The Voigt and Toloukian models are used to derive the material properties, where dependence of the properties to position and temperature is included. The one-dimensional transient heat transfer equation is established. The Crank-Nicholson approximation and Picard’s iterative method are used to solve this nonlinear equation using the GDQ numerical method in accordance with the temperature dependence of the material properties. After obtaining the temperature distribution along the thickness, it is possible to determine the thermal force and moment. Using the first-order shear theory to calculate the displacement field and the von Kármán form of geometry non-linearity, the equations of motion are determined. The Newton-Raphson iterative approach and the β -Newmark time estimate approach are used to solve the non-linear coupled equations of motion. The influencing factors on the reaction of the structure, such as the radius of the sphere and the length of the cylinder, the power law index, and the shell thickness are determined after the equations, techniques, and findings are validated.