Stress-strain state of reinforcing 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 with an 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 is used. True principal strains are expressed through dimensionless radial, annular, and normal stresses. An equation is obtained that describes the shape of the membrane after deformation, and the corresponding boundary conditions. Dimensionless stresses and the membrane shape after deformation are determined. Numerical calculations are carried out for various parameters of the problem.