一种新的无旋转等几何薄壳公式及相应的片边界连续性约束
A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
AI总结：
本文提出基于等几何有限元的无旋转非线性薄壳位移公式，支持多种三维积分与二维流形本构模型，并用罚函数和 Lagrange 乘子统一处理片间 $G^1$ 连续等约束，基准测试验证了其精度、鲁棒性与大变形性能。
摘要：
本文提出了一种基于等几何有限元的、用于无旋转薄壳的通用非线性计算公式。它是一种基于位移的公式，允许使用一般材料模型。该公式支持广泛的本构定律，既包括通过数值积分从现有三维连续体中提取的壳模型，也包括直接以二维流形形式表述的模型，如 Koiter、Canham 和 Helfrich 模型。此外，本文利用罚函数法和 Lagrange 乘子法，提出了一种统一方法，用于强制片与片之间的 $G^1$ 连续性、固定曲面折痕之间的角度、强制对称条件以及规定旋转 Dirichlet 边界条件。该公式完全在有限元描述的自然曲线坐标系中进行阐述，从而有助于高效的计算实现。它将现有的等几何薄壳公式作为特例包含在内。文中考虑了若干经典数值基准算例，以证明所提公式的鲁棒性和准确性。所给出的本构模型，特别是不需要任何厚度积分的简单混合 Koiter 模型，即使在大变形情况下也表现出优异性能。
英文摘要：
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a wide range of constitutive laws, including both shell models that are extracted from existing 3D continua using numerical integration and those that are directly formulated in 2D manifold form, like the Koiter, Canham and Helfrich models. Further, a unified approach to enforce the $G^1$-continuity between patches, fix the angle between surface folds, enforce symmetry conditions and prescribe rotational Dirichlet boundary conditions, is presented using penalty and Lagrange multiplier methods. The formulation is fully described in the natural curvilinear coordinate system of the finite element description, which facilitates an efficient computational implementation. It contains existing isogeometric thin shell formulations as special cases. Several classical numerical benchmark examples are considered to demonstrate the robustness and accuracy of the proposed formulation. The presented constitutive models, in particular the simple mixed Koiter model that does not require any thickness integration, show excellent performance, even for large deformations.
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