On thermo-mechanical nonlinear behaviour of shallow shells

Abstract

The structural performance of thin shells is largely dictated by their curvature and the degree of lateral restraint at the shell edges. The present study is an attempt to theoretically investigate the influence of such factors on nonlinear thermo-mechanical response of shallow shells with single and double curvatures. For the mechanical loading, a transverse load is assumed and for the thermal loading, a through-depth thermal gradient is applied on the shallow shell. Two types of boundary conditions are considered for the shallow shell, both of which constrain transverse deflections of the shell but allow rotations parallel to the shell boundaries to be free. One of the boundary conditions permits lateral translation (laterally unrestrained) and the other one does not (laterally restrained). The fundamental nonlinear equations of shallow shells are derived based on the quasi-static conditions. The validity and reliability of the proposed approach is assessed by calculating several numerical examples for shallow shells under various mechanical and thermal loads. It is found that the proposed formulation, in particular, can adequately capture the nonlinear behaviour of laterally restrained shallow shells.