Stability analysis of viscoelastic thin shallow hyperbolic paraboloid shells

The stability of linearly viscoelastic flexible shallow hyperbolic paraboloid shell is analysed under transverse load. Allowances are made for geometrical nonlinearity and initial imperfections of the surface shape. By application of the method of finite differences with respect to geometrical variables and the method of differentiation with respect to a parameter (time) the solution for the system of equilibrium non-linear integro-differential equations is reduced to Cauchys problem which can be solved numerically. The critical time was shown to depend on the load, curvature, initial imperfections and edge elements compressibility. Critical loads for an outlying time moment are determined.