Static and vibration analyses of laminated conical shells under various boundary conditions using a modified scaled boundary finite element method

In this paper, a modified scaled boundary finite element method (SBFEM) is developed to study static and vibration behaviors of laminated conical shells under the conical coordinate system. In the modified SBFEM, the geometry of the conical shell is defined entirely by scaling the internal surface of the structure. This approach eliminates geometric errors caused by discretization, thereby enhancing modeling accuracy. The three-dimensional problem is simplified to a twodimensional analysis since discretization is only applied to the boundary of the computational domain. Additionally, the semi-analytic property of the SBFEM allows for the derivation of a linear analytical solution for the laminated conical shell in the radial direction. First, a scaled boundary coordinate system for the scaling surface is established, and a second-order scaled boundary finite element governing equation with variable coefficients is derived for a single layer of the conical shell using the principle of virtual work. Next, the governing equation is transformed into a first-order system by introducing a combined vector of displacement and nodal force, and the stiffness matrices for each layer of the laminated conical shell are obtained using the precise integration method. Finally, an overall analysis of the laminated structure is conducted by assembling each single-layer structure while considering the continuity boundary condition at interfaces. Static and vibration analyses of laminated conical shells are conducted, and the results are compared with those from the literature to demonstrate the adaptability and convergence of the proposed method. Several numerical examples are presented to examine the effects of various geometric parameters, such as thickness, length, semi-vertex angles, layup directions, and stacking sequences, on the responses of the structure.