A methodology for modeling a rotating paraboloidal thin-shell structure attached to a spacecraft body is proposed considering its geometric nonlinear effect. Instead of using conventional shell elements to discretize the paraboloidal thin-shell in the Cartesian coordinate, the paraboloidal coordinates in the meridional, circumferential and normal directions are employed to completely express the deformations of the curved thin-shell. Then, explicit expressions for the generalized elastic forces and stiffness varying matrices are deduced on the basis of exact strain-displacement relations. And, the rigid-flexible coupled dynamic model for the flexible multibody system is derived by the principle of virtual work. In contrast with the previous modeling approaches, the present method shows an advantage in avoiding large calculation quantity of nonlinear stiffness matrix due to more formalized. Furthermore, a full analysis with specific numerical simulation is achieved by using the present model and conventional shell model, respectively. All simulation results obtained by the two modeling methods verify the correctness and better convergence of the proposed methodology.

中文翻译：

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抛物线形弯曲壳单元附加到航天器机构上的旋转抛物线形薄壳附件的非线性动力学建模

考虑到几何形状的非线性效应，提出了一种模拟旋转的抛物面形薄壳结构的方法。代替使用常规的壳单元在笛卡尔坐标中离散抛物线形薄壳，而是使用子午线，子午线，圆周和法线方向上的抛物线形坐标来完全表达弯曲的薄壳的变形。然后，在精确的应变-位移关系的基础上，推导了广义弹性力和刚度变化矩阵的明确表达式。并且，通过虚拟工作原理推导了柔性多体系统的刚柔耦合动力学模型。与以前的建模方法相比，该方法在形式化方面避免了非线性刚度矩阵计算量大的优点。此外，分别使用本模型和常规壳模型，可以进行具有特定数值模拟的全面分析。通过两种建模方法获得的所有仿真结果都证明了所提出方法的正确性和更好的收敛性。