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Geometrically nonlinear multi-patch isogeometric analysis of spatial Euler-Bernoulli beam structures

机译:空间欧拉 - 伯努利光束结构的几何非线性多贴片异步分析

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This study presents a novel isogeometric Euler-Bernoulli beam formulation for geometrically nonlinear analysis of multipatch beam structures. The proposed formulation is derived from the three-dimensional continuum theory where the beam axis and the director vectors of cross-sections are used to characterize beam configurations. The translational displacements of the beam axis and the axial cross-sectional rotation along the beam axis are considered as unknown kinematics. The orthogonality between the cross-sections and the beam axis is satisfied by using the smallest rotation mapping for the description of finite cross-sectional rotations. The use of the smallest rotation mapping reduces the nonlinearity of the employed strain measurements with respect to the unknown kinematics and offers highly efficient linearization. Furthermore, a penalty-free approach is introduced to deal with rigid connections in multi-patch beam structures in the context of geometrically nonlinear analysis. A novel nonlinear transformation between the total cross-sectional rotation and the unknown kinematics is derived, which facilitates the use of the total cross-sectional rotations at the ends of patches as discrete unknowns. This approach also allows straightforward enforcement of rotational boundary conditions. The proposed formulation is investigated by several well-established examples and great accuracy and efficiency are observed. (C) 2021 ElsevierB.V. All rights reserved.
机译:该研究提出了一种新的异构型欧拉-Bernoulli光束配方,用于多束结构的几何非线性分析。所提出的配方来自三维连续性理论,其中横截面和横截面的导向器矢量用于表征光束配置。梁轴的平移位移和沿着梁轴的轴向横截面旋转被认为是未知的运动学。通过使用用于有限横截面旋转的描述的最小旋转映射来满足横截面和梁轴之间的正交性。使用最小的旋转映射减少了与未知的运动学相对于未知的运动学的非线性的非线性,并提供高效的线性化。此外,引入了一种可靠的方法,以在几何非线性分析的背景下处理多跳线结构中的刚性连接。推导出总横截面旋转和未知运动学之间的新型非线性变换,这有利于在贴片的末端使用的总横截面旋转作为离散未知。该方法还允许直接执行旋转边界条件。通过若干良好的实例研究了所提出的制剂,观察到的良好准确性和效率。 (c)2021 elsevierb.v。版权所有。

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