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Transversally higher-order interpolating polynomials for the two-dimensional shear deformable ANCF beam elements based on common coefficients
Multibody System Dynamics ( IF 3.4 ) Pub Date : 2020-11-30 , DOI: 10.1007/s11044-020-09768-4
Chun H. Zhao , Kang W. Bao , Yu L. Tao

The polynomial representation for describing the displacement field of the elements is the main factor that determines the performance of the shear deformable beam elements based on the absolute nodal coordinate formulation (ANCF). In order to resolve the locking problem of the ANCF beam elements, the transversally higher-order polynomial representation has been investigated frequently and applied to the displacement field of the elements by increasing the nodal coordinates of the beam elements. In this paper, transversally higher-order interpolating polynomials are added into the polynomial displacement field of the elements by using common coefficients which mean that the coefficients between the higher-order longitudinal and transversal polynomial components are common. The implementation does not require the increase of the nodal coordinates. Two new kinds of two-dimensional transversally higher-order ANCF beam elements are formulated by common coefficients. The effect of transversally higher-order interpolating polynomials on the performance of the proposed ANCF beam elements is studied by means of certain static and dynamic problems. It is shown that the transversally quadratic order polynomial component \(y^{2}\) introduced by common coefficients can also relieve the problem of Poisson locking, and the proposed beam elements are effective and accurate in the static and dynamic analysis.



中文翻译:

基于共同系数的二维剪切可变形ANCF梁单元的横向高阶插值多项式

用于描述单元位移场的多项式表示法是基于绝对节点坐标公式(ANCF)确定可剪切变形梁单元性能的主要因素。为了解决ANCF梁单元的锁定问题,已经对横向高阶多项式表示法进行了研究,并通过增加梁单元的节点坐标将其应用于单元的位移场。在本文中,通过使用公共系数将横向高阶插值多项式添加到元素的多项式位移域中,这意味着高阶纵向和横向多项式分量之间的系数是公共的。该实现不需要增加节点坐标。两种新的二维横向高阶ANCF梁单元由共同系数表示。通过某些静态和动态问题,研究了横向高阶插值多项式对所提出的ANCF梁单元性能的影响。证明了横向二次多项式分量常用系数引入的\(y ^ {2} \)也可以缓解泊松锁定问题,并且所提出的梁单元在静态和动态分析中都是有效且准确的。

更新日期:2020-12-01
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