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

Abstract

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.

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

“…Recent decades have, following the pioneering lead by Basset [85], witnessed the introduction of second-and third-order shear deformation theories (TSDT), entailing continuity of quadratic and cubic, respectively, distribution, of the surface-parallel (in-plane for flat panels) displacement components through the laminate thickness [19], see for detailed reviews by Reddy [19], and Chaudhuri and Kabir [86] for the decades prior to 2000, and Giunta, et al [87], and Chaudhuri and Oktem [88,89], thereafter.…”

“…It has been noted earlier that for cross-ply laminates, while the former can only produce particular solutions for very specific set of boundary constraints [88], i.e. the SS3 prescribed at all four edges, the latter essentially solves a curved or straight beam type of boundary-value problems, because of the SS3 being prescribed at the remaining two opposite edges; see Appendix A for definition of various boundary constraints.Oktem and co-workers [88][89][99][100][101][102][103][104][105] presented boundary-discontinuous type double Fourier series solutions of highly coupled system of partial differential equations (relating to cross-ply laminated plates/shells) subjected to various boundary conditions. Needless to state, Navier [19,90,91] and Levy-type solutions [19,[92][93][94][95][96][97][98] to thick cross-ply flat and curved panels serve as special cases of the above.…”

“…( 7) into equilibrium equations given by Eqs. (A3) supplies the following five highly coupled fourth-order governing partial differential equations [89,96]. 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:…”

“…m Y , in terms of the unknown boundary Fourier coefficients , , m m n a b c and n d , defined in Eqs. (D1a, b)below[89,96,100], in a manner outlined in Figure2.These Fourier coefficients are then substituted in natural boundary conditions, given by Eqs (17),. thus reducing the size n a , n b , etc.…”