Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells

Abstract

Closed-form formulations of 2D higher-order shear deformation theories for the thermo-mechanical analysis of simply supported doubly curved cross-ply laminated shells are presented. Formulation includes the Sander’s theory for doubly curved shells. Two of the higher-order shear deformation theories account for the effects of both transverse shear strains/stresses and the transverse normal strain/stress, while the third includes only the effects of the transverse shear deformation. In these developments a realistic parabolic distribution of transverse shear strains through the shell thickness is assumed. The temperature variation considered in the formulation is uniform or sinusoidal over the surface and linearly varying through the thickness. Numerical results are presented for thermal and mechanical load cases in laminated composite and sandwich shallow shells. The closed-form solutions presented herein for laminated composite plate or shells are compared with the available 3D elasticity solutions for mechanical loading and it is believed that solutions for thermal loading will serve as bench mark in future.