Hygro-thermo-mechanical analysis of sandwich shallow shells considering the effects of transverse normal strain

The static response of softcore doubly-curved sandwich shallow shells under hygro-thermo-mechanical loading is presented herein using a fifth-order shell theory which considers the effects of transverse normal strains and stresses at the same time. The present theory accounts for non-linear variations of displacements. The strain-displacement relations take into account only small curvatures following a shallow shell description. The present theory ensured the traction-free boundary conditions at the top and the bottom faces of the shell. The governing equations along with the natural and essential boundary conditions are derived using the principle of virtual work. The governing equations are solved by using Navier's method. Three layered sandwich shallow shells of double curvature subjected to hygro-thermo-mechanical loading are analyzed. The accuracy and efficacy of the present theory are proved by applying it to the benchmark solutions available in the literature and then the present theory is extended for the analysis of softcore sandwich shells of double curvature. Since an exact 3D elasticity solution is not available for many such problems; this paper can be serving as a benchmark reference solution for future researchers working in this area.