Approximate Shell Theories

In order to confirm the soundness and accuracy of the proposed solution procedure presented in the preceding chapter, the results obtained through the equations of TDLTS are compared with those obtained through approximate shell theories for the same problem. For this purpose, two types of approximate shell theories are considered i.e., the Kirchhoff-Love shell theory is used to check the TDLTS based results for thick shells whereas the results from third-order refined shell theory is used for a comparative analysis of TDLTS based results for critical values of force/stress and time. The displacement fields, resulting strain expressions, integration of the equations, selection of solution functions for the system of equations, and the stability loss criteria for purely elastic and viscoleastic cases are given for both theories. The field equations for these theories are obtained using the equations and relations of the TDLTS. This is achieved by applying the averaging-integrating technique applied to the equilibrium equations, the boundary conditions, the constitutive relations, and the strain-displacement relations.