Nonlinear Theories for Imperfect Thin Shells: Application to Cylindrical Shells

摘要

Starting from the equilibrium equations, strain-displacement relations forimperfect shells, valid for large displacements, are derived. From these strain-displacement relations, approximate strain-displacement relations are derived by making certain simplifying assumptions. In particular, the middle surface strains are assumed small, the rotations are assumed moderately small, and the imperfection is assumed small. The obtained approximate membrane and bending strain tensors are used to formulate several nonlinear strain-displacement relations found in the literature in increasing stages of approximation. In particular, Sanders version and the Donnell-Mushtari-Vlasov version of the strain-displacement relations are given. These nonlinear strain-displacement relations are applied to the particular case of an imperfect cylinder. Additionally, Novozhilov's strain-displacement relations are given for that geometry. After deriving also the variational statement of equilibrium and the constitutive equations for a thin cylinder, a complete set of equations is obtained which are suitable as a basis for stability investigations of an imperfect cylinder under various loads.