Analytical and Numerical Solutions to Static Analysis of Moderately Thick Cross-Ply Plates and Shells

Abstract

This study aimed to provide a static solution to the boundary value problem presented by symmetric (0°/90°/0°) and antisymmetric (0°/90°) cross-ply composite, moderately thick shallow shells and plates (a special case of the shells) subjected to mixed-type unsolved boundary conditions. The boundary-discontinuous double Fourier series (BDM) method, in which displacements are expressed in trigonometric functions, is employed in a well-established framework. The analytical solution obtained using the BDM is compared with the successful integration of the generalized differential quadrature (GDQ) method for the static analysis of composite shells with a roller skate-type boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to simply supported constraints. Comprehensive results are presented in order to show the effects of curvature on the deflections and stresses of moderately thick shallow shells made up of symmetric and antisymmetric cross-ply laminated composite materials. The validity of the proposed model is authenticated through the available HSDT-based literature review, and the convergence characteristics are demonstrated. The changing trends of displacements and stresses are explained in detail by investigating the effect of various parameters such as lamination, material properties, the effect of curvature, etc. Based on the results obtained using the proposed static solution, analytical BDM results were found to be in very close agreement with the numerical GDQ method, especially for symmetric lamination. However, the results obtained using the BDM and GDQ methods for antisymmetric lamination show differences, possibly due to the presence of a discontinuity in the derivatives originating from the bending–stretching matrix in antisymmetric lamination. Important numerical results presented include the sensitivity of the predicted response quantities of interest to material properties, lamination, and thickness effects, as well as their interactions. The results presented here may also serve as benchmark comparison points with numerical solutions such as finite elements, boundary elements, etc.