Finite element formulation of spatially curved and twisted rods
Finite element formulation of spatially curved and twisted rods
复制标题
空间弯曲和扭曲杆的有限元公式
DOI：
10.1016/0045-7825(88)90021-7
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
H. Yi
中科院分区：
文献类型：
--
作者：
B. Tabarrok;M. Farshad;H. Yi
对于空间弯曲和扭转杆的一组控制方程组成的平衡方程和应变，位移和本构关系推导出的三个平移和三个旋转自由度。通过求解常应变和零应变状态下的应变位移关系，得到了杆的刚体模态和常应变模态。这些位移模式，然后被用作基础功能的有限元模型的发展。为了验证配方和元素矩阵，三个例子进行了分析，并在每种情况下的计算结果进行了比较，从离散模型表示，使用棱柱体Rakshenko杆元素。它被发现，弯曲的元素，这是几何精确的，产生更准确的结果，它消除了跳跃的一些力量的数量，所造成的不确定性的正常（和或切线，副法线），在节点。
For spatially curved and twisted rods a set of governing equations consisting of equilibrium equations and strain displacement and constitutive relations are derived in terms of three translational and three rotational degrees of freedom. By solving the strain displacement relations for constant and zero states of strain the rigid body and constant strain modes of the rod are obtained. These displacement modes are then used as basis functions for development of a finite element model. To verify the formulation and the elemental matrices, three examples are analyzed and in each case the computed results are compared with those obtained from a discrete model representation, using prismatic Timoshenko rod elements. It is found that the curved element, which is geometrically exact, yields more accurate results and it eliminates the jumps in some force quantities, caused by the indeterminacy of the normal (and or tangent, binormal), at the nodes.