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 two-dimensional 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.

中文翻译：

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使用改进的缩放边界有限元方法在各种边界条件下对层压圆锥壳进行静态和振动分析


本文开发了一种改进的缩放边界有限元方法 （SBFEM） 来研究锥形坐标系下层压锥形壳的静态和振动行为。在修改后的 SBFEM 中，圆锥壳的几何形状完全通过缩放结构的内表面来定义。这种方法消除了离散化引起的几何误差，从而提高了建模精度。三维问题被简化为二维分析，因为离散化仅适用于计算域的边界。此外，SBFEM 的半解析特性允许在径向上推导出层压圆锥壳的线性解析解。首先，建立了缩放面的缩放边界坐标系，并利用虚拟功原理推导了圆锥壳单层的二阶缩放边界有限元控制方程。然后，通过引入位移和节点力的组合矢量，将控制方程转换为一阶系统，并使用精确积分法获得层压锥形壳每层的刚度矩阵。最后，通过组装每个单层结构，同时考虑界面处的连续性边界条件，对层合结构进行整体分析。对层压锥形壳进行了静态和振动分析，并将结果与文献结果进行了比较，以证明所提方法的适应性和收敛性。 文中提供了几个数值示例，以检查各种几何参数（如厚度、长度、半顶点角度、铺层方向和堆叠顺序）对结构响应的影响。