Application of the variational theorem for creep of shallow spherical shells

Abstract

The variational theorem for creep is used to study the creep deflections and collapse times for simply supported thin shallow spherical shells under uniform external pressure. The initial and subsequent forms of the stress resultants and displacements are obtained with the aid of the elastic theory of thin shallow spherical shells. The variational theorem for creep leads to a set of simultaneous ordinary differential equations with prescribed initial conditions. Numerical solutions are generated by means of the Runge-Kutta method. Theoretical predictions for creep deflections and collapse times are compared with experimental data for five test shells at each of three different pressure levels for Type 6/6 Nylon. It was found that the theory predicts creep deflections that are consistently smaller than the experimental values, whereas the theoretical collapse times are consistently larger than the experimental collapse times. The discrepancy between the theoretical predictions for creep deflections and collapses times and the experimental data is believed to be due largely to the deviations which occur between the theoretical and actual stress and displacement mode shapes with the passage of time. Closer agreement should be expected when more time flexibility is built into these mode forms.