Stress intensification in a viscoelastic plate on a Winkler foundation and under a large thermal gradient

Abstract

A thin viscoelastic plate on a Winkler foundation is subjected to vertical loads. Its response is strongly affected by the presence of a vertical temperature gradient which causes a very pronounced change in the viscosity coefficient through the plate thickness. While eventually the entire load will be transferred to the underlying foundation, during the time dependent deformation process it is possible that some bending stresses will actually increase rather than decrease as would normally be expected with this relaxation process. The rationale for this behavior lies in the competition between the two physical processes of a) the load transfer to the foundation causing an overall relief of the bending moment and thus the bending stress and b) the rapid relaxation of bending stress in the hot lower portion of the plate causing the colder upper portion to carry a larger share of that portion of the bending moment still carried by the plate. The simple case of a clamped circular plate of a metallic material and subjected to a uniform load is used to illustrate this behavior. Certain simplifications are made to allow an analytic solution; these simplifications do not alter the basic behavior. In the present case, these simplifications are the neglect of Poisson's ratio effects and the assumption of a linear “equivalent” viscoelastic material behavior. This latter point is discussed in an appendix. Numerical solutions containing more general behavior indicate that the basic behavior is still well modeled even with these assumptions.