This study presents first a relatively lesser studied topic of the role played by surface-parallel restraints in determining the response of simply supported thick to thin doubly curved cross-ply panels of rectangular plan-form, modeled using a third order shear deformation theory, quantified by way of the difference between full and absent surface-parallel edge restraints. Mathematically speaking, this corresponds to the difference between complementary solutions to mixed boundary-value problems, resulting from two extreme sets of surface-parallel restraints. Of special interest is the threeway interaction of the membrane action due to curvature with the surface-parallel boundary constraint as well as the higher-order (resp. first-order) bending-stretching coupling producing beam-column/tie-bar type softening/hardening effects in thick (respectively thin) asymmetric cross-ply panels. Comparison with other popular shear deformation theories, such as the layer-wise constant shear-angle theory or zig-zag theory and first order shear deformation theory, also constitutes an important focus of this investigation. Results for cross-ply plates are regenerated in order to show the severity of the effect of curvature, especially in the thin shell regime.

An analytical (exact in the limit) solution to the boundary-value problem of deformation of a finite-dimensional general cross-ply thick hyperbolic-paraboloidal panel, modeled using a third order shear deformation theory, is presented. Of special interest is the issue of cylindrical panel-like response, in the presence of full surface-parallel constraints at all four edges of a thick antisymmetric cross-ply panel of negative Gaussian curvature. Interaction of the membrane action due to negative Gaussian curvature with the third order (respectively, first-order) bending-stretching coupling producing beam-column/tie-bar type softening/hardening effects in thick (respectively, thin) cross-ply panels also constitutes an important focus of this investigation.