Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation
Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation
复制标题
DOI：
10.1115/1.4000793
复制
发表时间：
2010-04
影响因子：
2
通讯作者：
H. Sugiyama;H. Koyama;Hiroki Yamashita
中科院分区：
文献类型：
--
作者：
H. Sugiyama;H. Koyama;Hiroki Yamashita
本文将绝对节点坐标形式的亏梯度梁单元推广到用于多体系统分析的曲梁，并与完全参数化的曲梁单元和经典的大位移梁单元的增量求解方法进行了比较。应变分量是相对于初始弯曲构形定义的，并由弧长坐标描述。格林应变用于纵向拉伸，而曲率的材料度量用于弯曲。结果表明，曲梁的应变可以用梯度变换表示为单元坐标系中定义的应变，用一维Almansi应变消除了初始弯曲位形上的应变影响。这一性质可以有效地与绝对节点坐标公式采用的非增量解程序一起使用。文中给出了几个数值算例，以说明本文提出的亏梯曲梁单元的性能。结果表明，与完全参数化梁单元和经典的大位移梁单元相比，该单元具有更好的单元收敛性能。
In this investigation, a gradient deficient beam element of the absolute nodal coordinate formulation is generalized to a curved beam for the analysis of multibody systems, and the performance of the proposed element is discussed by comparing with the fully parametrized curved beam element and the classical large displacement beam element with incremental solution procedures. Strain components are defined with respect to the initially curved configuration and described by the arc-length coordinate. The Green strain is used for the longitudinal stretch, while the material measure of curvature is used for bending. It is shown that strains of the curved beam can be expressed with respect to those defined in the element coordinate system using the gradient transformation, and the effect of strains at the initially curved configuration is eliminated using one-dimensional Almansi strain. This property can be effectively used with a nonincremental solution procedure employed for the absolute nodal coordinate formulation. Several numerical examples are presented in order to demonstrate the performance of the gradient deficient curved beam element developed in this investigation. It is shown that the use of the proposed element leads to better element convergence as compared with the fully parametrized element and the classical large displacement beam element with incremental solution procedures.