Finite element analysis of huge and/or complicated structures often requires long times and large computational expenses. Superelements are huge elements that exploit the deformation theory of a specific problem to provide the capability of discretizing the problem with minimum number of elements. They are employed to reduce the computational cost while retaining the accuracy of results in FEM analysis of engineering problems. In this research, a new shell superelement is presented to study linear/nonlinear static and free vibration analysis of spherical structures with partial or full spherical geometries that exist in many industrial applications. Furthermore, this study investigates the effects of changing the superelement size and its number of nodes on solution accuracy. The governing equations of composite spherical shells are derived based on the first-order shear deformation theory and considering large deformations. For solving the nonlinear governing equations, the tangent stiffness matrix has been extracted and the Newton–Raphson method is employed. The capability of the presented shell superelement is investigated in several problems under linear/nonlinear static and free vibration analysis. The results acquired by the presented shell superelements are compared with available results in the literature and conventional shell elements in a commercial software. Results comparisons reveal high accuracy at a reduced computational cost in the superelement model.

中文翻译：

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用于复合球壳大变形和自由振动分析的壳超单元的开发

巨大和/或复杂结构的有限元分析通常需要很长时间和大量计算费用。超单元是利用特定问题的变形理论来提供以最少单元数离散问题的能力的巨大单元。它们用于降低计算成本，同时保持工程问题 FEM 分析结果的准确性。在这项研究中，提出了一种新的壳超单元来研究许多工业应用中存在的具有部分或全球形几何形状的球形结构的线性/非线性静态和自由振动分析。此外，本研究调查了改变超单元尺寸及其节点数量对求解精度的影响。基于一阶剪切变形理论并考虑大变形，推导出复合材料球壳的控制方程。为了求解非线性控制方程，提取了切线刚度矩阵并采用了 Newton-Raphson 方法。在线性/非线性静态和自由振动分析下的几个问题中研究了所提出的壳超单元的能力。将呈现的壳超单元获得的结果与文献中的可用结果和商业软件中的常规壳单元进行比较。结果比较揭示了超单元模型中计算成本降低的高精度。已经提取了切线刚度矩阵并采用了 Newton-Raphson 方法。在线性/非线性静态和自由振动分析下的几个问题中研究了所提出的壳超单元的能力。将呈现的壳超单元获得的结果与文献中的可用结果和商业软件中的常规壳单元进行比较。结果比较揭示了超单元模型中计算成本降低的高精度。已经提取了切线刚度矩阵并采用了 Newton-Raphson 方法。在线性/非线性静态和自由振动分析下的几个问题中研究了所提出的壳超单元的能力。将呈现的壳超单元获得的结果与文献中的可用结果和商业软件中的常规壳单元进行比较。结果比较揭示了超单元模型中计算成本降低的高精度。将呈现的壳超单元获得的结果与文献中的可用结果和商业软件中的常规壳单元进行比较。结果比较揭示了超单元模型中计算成本降低的高精度。将呈现的壳超单元获得的结果与文献中的可用结果和商业软件中的常规壳单元进行比较。结果比较揭示了超单元模型中计算成本降低的高精度。