Analytical solution for stability analysis of joined cross-ply thin laminated conical shells under axial compression

The present research considers the stability and corresponding modes of two axially compressed joined cross-ply laminated conical shells. The joined conical shells are the general case of a wide area of joined structures, including cylinder-cone, cone-plate, cylinder-plate, stepped thickness cone and stepped thickness cylinder. The principle of minimum potential energy is applied to extract the equilibrium equations under the thin Donnell type shell theory assumptions. The analytical procedure is used to solve the equations by applying trigonometric and series responses in circumferential and meridional directions, respectively. To ensure from accuracy and correctness of the results, the finite element analysis is done for various stacking sequences and the analytical results are compared and validated with other literature and finite element results. Finally, the effects of some parameters including semi-vertex angles, meridional lengths, number of layers and various kinds of simply supported and clamped boundary conditions at both ends are studied.