Stability analysis of viscoelastic thin shallow hyperbolic paraboloid shells

The stability of linearly viscoelastic ~exible shallow hyperbolic paraboloid shell is analysed under trans! verse load[ Allowances are made for geometrical nonlinearity and initial imperfections of the surface shape[ By application of the method of _nite di}erences with respect to geometrical variables and the method of di}erentiation with respect to a parameter "time# the solution for the system of equilibrium non!linear integro!di}erential equations is reduced to Cauchy|s 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