Method for thermoviscoelastic stress analysis in concrete reactor vessels

This paper is concerned with the analysis of problems in thermoviscoelasticity. The displacement equations of equilibrium governing the behavior of stressed, isotropic, thermorheologically simple materials subjected to thermal variations are formulated with respect to integral constitutive equations. This leads to a system of three, second order, variable coefficient, partial differential equations in the spatial coordinates and integral equations in the time. The general problem is formulated within the framework of classical, uncoupled thermoviscoelastic theory. A solution to the general displacement equations of equilibrium is presented for a point symmetric temperature field and point symmetric boundary conditions.

The general theory is also formulated from the principle of virtual displacements. From the principle of virtual displacements, it is shown how exact, as well as approximate, solutions may be obtained. An example is included for the solution to an incompressible hollow cylinder subjected to an axisymmetric temperature field.