Transient analysis of thermo-mechanically shock loaded four-parameter power law functionally graded shells

Abstract

The present work identifies the mechanical and thermal response of ceramic–metal composed functionally graded cylindrical and spherical shells of revolution exposed to rapidly applied mechanical and thermal loads on their inner surface. The gradation of the constituent materials is done in the thickness direction of the FG shells according to four-parameter power laws. The mechanical and thermal properties of the constituent materials are considered to be temperature-dependent. Mori-Tanaka model is employed to obtain effective material properties based on the homogenization method. A nonlinear 1-D heat conduction equation is solved in each time-step of unconditionally stable Crank-Nicolson time integration scheme. Thereafter, an uncoupled thermoelastic finite element code based on higher-order shear deformation theory for shells and Newmark time integration scheme is developed in MATLAB environment. Numerical results considering the effect of the geometry of the shell, thermal boundary conditions, temperature-dependent material properties, different parameters of FGM laws, and thermomechanical load on the response characteristic of shells are presented. It was found that the oscillations of a thermomechanical shocked shell initially deviated from its quasi-static nature of response but started to oscillate about the quasi-static curve as its mean position on removal of the mechanical load.