On consistent Reissner beam formulation using quaternion algebra

机译：关于使用四元数代数的一致Reissner梁公式

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In the paper we present the Reissner beam theory in which the rotations are parametrized by the quaternions. From the generalized virtual work principle, where the unity constraint of the rotational quaternion is properly considered, and the consistent energy complements of the rotational quaternions are employed we derive the weak kinematic equations in the quaternion-based description. These equations are then employed in the same extended virtual work principle to obtaine the consistent and exact governing equations of the three-dimensional beam in terms of the quaternion algebra. The quaternion moment equilibrium equation is analysed, discussed and interpreted.

机译：在本文中，我们介绍了Reissner梁理论，其中旋转是由四元数参数化的。从广义虚拟工作原理出发，适当考虑旋转四元数的单位约束，并采用旋转四元数的一致能量补，我们在基于四元数的描述中得出了弱运动学方程。然后将这些方程式用于相同的扩展虚拟功原理，从而根据四元数代数获得三维束的一致且精确的控制方程式。对四元数矩平衡方程进行了分析，讨论和解释。

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《Recent researches in engineering mechanics, urban amp; naval transportation and tourism》|2012年|55-60|共6页
会议地点 Cambridge(GB);Cambridge(GB);Cambridge(GB);Cambridge(GB)
作者
EVA ZUPAN; DEJAN ZUPAN; MIRAN SAJE;
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University of Ljubljana Faculty of Civil and Geodetic Engineering Jamova 2, SI-1115 Ljubljana SLOVENIA;

University of Ljubljana Faculty of Civil and Geodetic Engineering Jamova 2, SI-1115 Ljubljana SLOVENIA;

University of Ljubljana Faculty of Civil and Geodetic Engineering Jamova 2, SI-1115 Ljubljana SLOVENIA;

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reissner beam theory; quaternion algebra; rotational quaternion; generalized virtual work principle; equilibrium equations; quaternion moment;

机译：Reissner梁理论四元数代数旋转四元数广义虚拟工作原理；平衡方程四元数矩;

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专利

1. On a virtual work consistent three-dimensional Reissner-Simo beam formulation using the quaternion algebra [J] . Zupan E., Saje M., Zupan D. Acta Mechanica . 2013,第8期

机译：在虚拟工作上使用四元数代数的三维三维Reissner-Simo光束公式
2. Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff-Love Theory Versus Simo-Reissner Theory [J] . Meier Christoph, Popp Alexander, Wall Wolfgang A. Archives of Computational Methods in Engineering . 2019,第1期

机译：细长梁的几何精确有限元公式：Kirchhoff-Love理论与Simo-Reissner理论
3. A BEM formulation based on Reissner's theory to perform simple bending analysis of plates reinforced by rectangular beams [J] . Fernandes GR, Konda DH Computational Mechanics: Solids, Fluids, Fracture Transport Phenomena and Variational Methods . 2008,第5期

机译：基于Reissner理论的BEM公式，可以对矩形梁加固的板进行简单的弯曲分析
4. REISSNER S MIXED VARIATIONAL THEOREM FOR LAYER-WISE REFINED BEAM MODELS BASED ON THE UNIFIED FORMULATION [C] . Erasmo Carrera, Alberto Garcia de Miguel, Alfonso Pagani, ASME international mechanical engineering congress and exposition . 2018

机译：基于统一公式的分层精化梁模型的Reissner混合变分定理
5. Thermodynamic Consistency of the Currently Used Beam Mathematical Models and Thermodynamically Consistent New Formulations for Bending of Thermoelastic, and Thermoviscoelastic Beams [D] . Mysore Krishna, Dhaval. 2019

机译：目前使用的光束数学模型的热力学稠度以及热弹性弯曲的热力学一致的新配方，以及热煤层和热扫描梁
6. Linear Algebraic Beamforming Design for Multiuser MISO Interference Channels: A Reduction in Search Space Dimension [O] . Sang Won Choi, Won-Yong Shin, Juyeop Kim 2018

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7. On a virtual work consistent three-dimensional Reissner–Simo beam formulation using the quaternion algebra [O] . Zupan, Eva, Saje, Miran, Zupan, Dejan 2013

机译：在虚拟工作中，使用四元数代数的三维三维Reissner-Simo光束公式

On consistent Reissner beam formulation using quaternion algebra

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