Generalized theory for the dynamic analysis of thin shells with application to circular cylindrical geometries

Abstract

A generalized theory is formulated for the analysis of thin shells of general curvatures based on the variational form of the Hamiltonian functional in conjunction with tensor calculus. Simplifying approximations and subtle inconsistencies made at the early stages of common classical formulations are avoided herein, and hence, the present treatment leads to field equations and boundary conditions that are accurate and consistent. The theory is then specialized to circular cylindrical shells. The well -known field equations of Flugge and Donnell-Mushtari-Vlasov (DMV) theories are recovered as consistent approximations from the present theory. Closed form solutions are then developed for the present and past cylindrical shell theories by Flugge, Timoshenko, and DMV. A comparative study is conducted to assess and quantify the effects of approximations made in classical theories on the predicted displacements and stresses.