Stateczność Grubościennej Rury Obciążonej Ciśnieniem Zewnętrznym

The problem is that of stability of a. thick-walled tube under nonhomogeneous deformation produced by hydraulic pressure. The material is assumed to be elastic, homogeneous, isotropic and incompressible.
The total strain is divided into two parts: finite initial and small additional part. The incompressibility conditions and the equilibrium equations constitute a set of four homogeneous linear differential equations with homogeneous boundary conditions. Further considerations are confined to the case of plane strain and the Mooney material. By separating the variables a single ordinary differential equation of the fourth order is obtained. The problem of stability loss is reduced to that of eigenyalues of a differential equation. As an illustration numerical computation is done for fixed values of the parameters α and λ. The deformation assumed corresponds to two different "critical thicknesses" of the tube.