Wyboczenie przy pełzaniu geometryczne nieliniowej powłoki kulistej

The problem under consideration is that of buckling of a geometrically nonlinear spherical shell of small rise made of a linear viscoelastic material, loaded by a constant external load. It is assumed that before the load is applied, the shell has a small local concavity constituting a small deviation from its ideal shape. The problem is treated as that of local buckling of a spherical shell under conditions of creep. The nonlinear equations of the problem are derived by assuming the form of the concavity and the form of the deflection of a deformed element of the shell. In order to determine the deflection of the centre of the concavity we solve the fundamental nonlinear equation in the operator form,
by applying the Galerkin method. In the general case of the physical law, if the operators involved in the fundamental equation are linear integral operators, this equation can be reduced to a set of linear integral recurrence equations obtained by perturbation. The small parameter has a geometric sense and is expressed in terms of the dimensions of the shell. Solutions are given for particular cases of viscoelastic bodies with a discussion of the results obtained. As a particular case we obtain the solution for the elastic shell. In conclusion the behaviour of the shell in the course of the creep process is discussed in function of the load and the physical properties of the material.