A theory of thin shells with finite displacements and deformations based on a modified Kirchhoff–Love model

A refined classical Kirchhoff–Love theory of thin shells with finite displacements and deformations is given that takes account of deformation in a transverse direction by introducing an additional unknown function to describe it. It is shown that the last of the three equilibrium equations for the moments obtained from the variational equation of the principle of virtual displacements serves to determine it. Constitutive relations are constructed for the internal forces and moments introduced into the treatment based on the introduction of the true Novoshilov stresses and strains into the discussion. The solution of problem of the static stability of a cylindrical shell made of a rubber-like incompressible material inflated by an internal pressure is given using the equations constructed. Chernykh's constitutive relations are used in its formulation.