Effects of Surface-Parallel Edge Restraints and Inter-laminar Shear on the Responses of Doubly Curved General Cross-Ply Panels

Abstract

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.

Cylindrical Panel Like Response of Fully Surface Parallel Restrained Simply Supported Hyperbolic Paraboloidal Thick General Cross-ply Panels

“…Third and more important, the present and future TSDT-based results for laminated anisotropic panels of negative Gaussian curvature can be compared with their counterparts computed using the zig-zag theory (or layer-wise constant shear angle theory (LCST))-based FEM [4,7,[81][82][83][84][85][86][87][88][89][112][113][114][115][116][117][118][119][120] in a manner akin to what has been reported in Chaudhuri and Oktem [69].…”

“…The constants, , , Substitution of Equations ( 7) into equilibrium equations given by Eqs. (A3) supplies the following five highly coupled fourth order governing partial differential equations [69,73]: In what follows, the above system of five partial differential equations is solved in conjunction with the SS4 type simply supported boundary condition, prescribed at the edges, 1 0, x = a , and 2 0, x = b , which are given as follows:…”

“…More recently, second-and third order shear deformation theories (TSDT), involving continuous inplane/surface-parallel displacements distribution through the thickness of thick laminated plates/shells, have become available in the literature to account for the through-thickness shear deformation. A thorough review on the historical development of TSDT-based laminated plates/shells is available in Reddy [6], Chaudhuri and Kabir [66] for the earlier years, and Oktem and Chaudhuri [67,68], Chaudhuri and Oktem [69] and Giunta, et al [70] for the more recent development on this topic.…”

“…Navier type solutions to various third order and other type (e.g., trigonometric) of shear deformation theories, which can at best be regarded as particular solutions, have been extensively employed in the literature; see, e.g., Reddy [6], and Mantari, et al [71]. Boundary-discontinuous type double Fourier series solutions, in contrast, constitute complete (complementary and particular) solutions to the boundary-value problems of TSDT-based cross-ply laminated plates and shells [67][68][69]. The precise mathematical premises of the boundary-discontinuous type double Fourier series approach to solution of completely coupled system of partial differential equations subjected to admissible general boundary conditions are available in Chaudhuri [72,73].…”

“…Before presenting numerical results for saddle-shaped panels, those pertaining to symmetric and anti-symmetric cross-ply (R 1 = R 2 = ∞) plates [101] as well as spherical (R 1 = R 2 ) panels [69], with the same boundary conditions have been reproduced first. Additionally, (Figure 8) of Oktem and Chaudhuri [101] displays the convergence (with m = n) of normalized transverse displacement (deflection), Similar rapid convergence is observed for their spherical panel counterparts for m = n ≤ 10 in Figure 2 of Chaudhuri and Oktem [69]. For the distributed patch load, applied over one-fourth of the area of the panel, the applied pressure term used in the computation is given as follows: (under patch load) with a/h ratio.…”