Stress-Strain State of Sealing Rubber Membranes at Large Deformations

This paper describes a stress state of membranes of variable thickness at large deformations, namely the deformation of round continuous anisotropic and isotropic membranes of initial variable thickness, which are under the action of a uniformly distributed load. It is assumed that the membrane materials are elastic, and generalized Hooke’s law is used to describe their behavior. This problem is solved using the equation of equilibrium of the membrane element. True principal strains are expressed through dimensionless radial, annular, and normal stresses. An equation that describes the shape of the membrane after deformation and the corresponding boundary conditions are obtained. The dimensionless stresses and the shape of the membrane after deformation are determined. Numerical calculations are carried out for various parameters of the problem.