Equilibrium of nonlinearly elastic shells of rotation with isolated disclination

Abstract The problem of large strains of shells of revolution containing disclinations is studied based on the 6‐parameter nonlinear theory of elastic shells known as the Cosserat model. The concept of isolated disclination in a shell of revolution is introduced by applying the general theory of Volterra dislocations in multi‐connected elastic shells. The Frank vector of this disclination is oriented along the revolution axis of the shell. A special substitution in the general system of nonlinear equilibrium equations is proposed to reduce the problem of large strains of rotational shells with disclination to a nonlinear boundary value problem for a system of ordinary differential equations. This allows us to find for the first time an exact analytical solution to the problem of equilibrium for a shell with disclination in the framework of the membrane theory of Cosserat shells. In the case of a general 6‐parameter model, a numerical solution to the problem of disclination in a closed spherical shell loaded with internal pressure is given. The peculiarities of the stress‐strain state of the shell due to the influence of disclination are analysed.