Contact Problems Of Elastic Shells

Abstract

In this paper axially symmetric interaction of the shells of rotation made from elastic materials with the rigid bodies of rotation have been considered. For this class of problems the variational statements have been suggested on the basis of mathematical theory of variational inequalities. Large deformations of rubber are described by the constitutive equations of incompressible elastic material. Specific potential energy of the deformation of isotropic material is the function of two invariants of Cauchy-Green's deformations measure. The generalised solution of the contact problems is reduced to the problem of conditional minimisation of the non-linear functional. The solution of the problem of non-linear programming is performed by the method of local variations and when this method is used it is easy to change the form of rigid body and deformations potential view. Numerical solution is performed for rubber shell of the device which disconnects the collector sections. Under the action of the internal pressure the rubber shell expands, makes contact with the cylindrical surface of the collector.