Buckling of Spherical Viscoelastic Shells

The creep buckling of thin nonshallow spherical shells is treated, the material of which is assumed to be isotropic and linearly viscoelastic with special temperature dependence of its mechanical properties so as to fit the thermorheologically simple body model. The shell is subjected to uniform external pressure smaller than the classical buckling pressure for corresponding elastic shells. The prebuckling stress state is assumed to be the membrane state, and total deflections are less than or equal to the shell thickness. The classical stability criteria, uniqueness of equilibrium, is used in formulating the problem, defined by a linear integrodifferential equation in terms of displacement field W, and describing the adjacent equilibrium configuration, and it is assumed to be a function of coordinates and time. A first-step approximation to the governing equation is derived and used to determine the external critical pressure loading as a function of temperature, time, and shell geometry. For a shell made of a three-element model material a safe load limit is established.