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Simple and Efficient Tetrahedral Finite Elements With Rotational Degrees of Freedom for Solid Modeling

机译:具有旋转自由度的简单高效的四面体有限元实体建模

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摘要

A mixed variational principle and derivation of two simple and efficient tetrahedral finite elements with rotational degrees of freedom (DOF) are presented. Each element has four nodes. Every node has six DOF, which include three translational and three rotational DOF. Each element is capable of providing six rigid-body modes. The rotational DOF are based on the displacement formulation, while the translational DOF are hinged on the hybrid strain Hellinger-Reissner functional. Explicit expressions for stiffness matrices are obtained. Element performance has been evaluated with benchmark problems, indicating that they have superior accuracy compared with other lower-order tetrahedral elements.
机译:提出了混合变分原理和两个简单​​有效的具有旋转自由度(DOF)的四面体有限元的推导。每个元素都有四个节点。每个节点都有六个自由度,其中包括三个平移和三个旋转自由度。每个元素都能够提供六个刚体模式。旋转自由度基于位移公式,而平移自由度则取决于混合应变Hellinger-Reissner功能。获得了刚度矩阵的显式表达式。已对元素性能进行了基准问题评估,表明与其他低阶四面体元素相比,它们具有更高的精度。

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