Analytical Solution of the Coupled Dynamic Thermoelasticity Problem in a Hollow Cylinder

The fully classical coupled thermoelasticity problem in a thick hollow cylinder is solved using analytical methods. Finite Hankel transform, Laplace transform and a contemporary innovative method are used to solve the problem and presenting closed-form relations for temperature and stress distribution. To solve the energy equation and the structural equation, on the inner and the outer surfaces of the cylinder, time-dependent thermal and mechanical boundary conditions are applied. The Dirichlet boundary condition which represents temperature, is considered to solve the energy equation and the Cauchy boundary condition which represent traction, is considered for the equation of motion. Two cases are studied numerically, pure mechanical load and pure thermal load. In plotting the results for the case of prescribing pure mechanical load in spite of not applying any thermal load induced temperature can be seen in the temperature history figure. Due to solving the elastodynamic problem, the elastic and the thermoelastic stress wave propagation into the medium and the reflection were observed in the plotted results.