Large strains of cylindrical and spherical elastic shells with distributed dislocations

Based on the 6-parameter nonlinear theory of elastic shells, the influence of continuously distributed dislocations on the deformation of a thin circular cylinder loaded with hydrostatic pressure, longitudinal force, and torque and a closed spherical shell loaded with tension and a distributed couple load is studied. For these structures, exact solutions of the equilibrium equations are constructed valid for large strains and rotations. The relative simplicity of the obtained solutions allows using them in experimental studies of the mechanical behavior of two-dimensional materials with defects. •Nonlinear micropolar shells model two-dimension systems with distributed dislocations.•The semi-inverse method allows obtaining the exact solution of equilibrium equations.•Possibility of pure moment state of the closed spherical shell demonstrated.