Transient thermal response in thick orthotropic hollow cylinders with finite length: High order shell theory

The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations through the thickness, respectively. It is important that the radial stress is approximated by a cubic expansion satisfying the boundary conditions at the inner and outer surfaces, and the corresponding strain should be least-squares compatible with the strain derived from the strain-displacement relation. The equations of motion are derived from the integration of the equilibrium equations of stresses, which are solved by precise integration method (PIM). Numerical results are obtained, and compared with FE simulations and dynamic thermo-elasticity solutions, which indicates that the high order shell theory is capable of predicting the transient thermal response of an orthotropic (or isotropic) thick hollow cylinder efficiently, and for the detonation tube of actual pulse detonation engines (PDE) heated continuously, the thermal stresses will become too large to be neglected, which are not like those in the one time experiments with very short time.