Differential Cubature Method for Static Solution of Laminated Shells of Revolution with Mixed Boundary Conditions

The bending analysis of laminated shells of revolution, such as spherical, conical and cylindrical panels, is carried out utilizing the differential cubature method (DCM). To do so, a general software based on the DCM is developed which can tackle shells of revolution with symmetric and unsymmetric lamination sequence. Analysis of shells with general Loading and various combinations of clamped, simply supported, free and mixed boundary condition, may be carried out having acceptable accuracy. Using first order shear deformation theory, fifteen first order partial differential equations are obtained which contain fifteen unknowns in terms of displacements, rotations, moments and forces. Utilizing all of these equations results in the capability of the method to deal with any kinds of boundary conditions. Comparison of the results obtained by the DCM, shows very good agreement with the results of other numerical and analytical methods, while having less computational effort.

POSTBUCKLING OF LAMINATED SHELLS OF REVOLUTION WITH MERIDIONAL CURVATURE UNDER THERMAL AND MECHANICAL LOADS

A study on the influence of meridional curvature on the buckling and postbuckling behavior of cross-ply laminated shells of revolution subjected to thermal and mechanical loads is carried out using the semianalytical finite element method. The nonlinear equations are solved using the Newton–Raphson iterative technique. The adaptive displacement control method is employed to trace the equilibrium path. Examined herein are the effects of positive and negative meridional curvature, the number of layers and the number of circumferential waves on the buckling/postbuckling behavior of cross-ply laminated, simply supported shells under thermal, external pressure, torsional and axial loadings. It is found that the critical load increases with the increase in the rise-to-radius ratio of positive meridional curvature shells for the loading cases considered. The critical temperature, torsional, axial loads decrease and the critical external pressure increases with increasing magnitude of the rise-to-radius ratio of negative meridional curvature shells. The postbuckling response of shells exposed to a uniform temperature rise is of a hardening nature for both positive and negative meridional curvature cases. Shells subjected to external pressure show a softening type of initial postbuckling response for positive meridional curvature, and a hardening type of postbuckling response for negative meridional curvature. The qualitative nature of postbuckling characteristics for torsional and axial loading cases may be softening, hardening or initially softening and later hardening, depending upon the combined influence of the rise-to-radius ratio, the number of circumferential waves and the number of layers.