Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams
Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams
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DOI：
10.1016/j.cma.2014.06.023
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发表时间：
2014-09
影响因子：
7.2
通讯作者：
Cédric Adam;S. Bouabdallah;M. Zarroug;H. Maitournam
中科院分区：
文献类型：
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作者：
Cédric Adam;S. Bouabdallah;M. Zarroug;H. Maitournam
本文提出了一个通用的数学框架，用于在基于B-Spline/NURBS的等距分析中定义新的求积规则。结果表明，面片内各单元的高阶连续性比C0有限元具有更高的精度和更好的时间效率。不幸的是，最大的规律性加剧了厚结构元素中的剪切和膜锁定。给出了一维梁问题的改进选择降阶积分格式，该格式的基函数为二阶和三阶，可以方便地推广到高阶。由此得到的B-Spline/NURBS有限元没有膜和横向剪切锁定。此外，不会产生零能级模式。通过悬臂梁在分布弯矩作用下的经典试验，对该方法的性能进行了评估，并与Lagrange次积分有限元进行了比较。
A general mathematical framework is proposed, in this paper, to define new quadrature rules in the context of B-spline/NURBS-based isogeometric analysis. High order continuity across the elements within a patch turned out to have higher accuracy than C 0 finite elements, as well as a better time efficiency. Unfortunately, a maximum regularity accentuates the shear and membrane locking in thick structural elements. The improved selective reduced integration schemes are given for uni-dimensional beam problems, with basis functions of order two and three, and can be easily extended to higher orders. The resulting B-spline/NURBS finite elements are free from membrane and transverse shear locking. Moreover, no zero energy modes are generated. The performance of the approach is evaluated on the classical test of a cantilever beam subjected to a distributed moment, and compared to Lagrange under-integrated finite elements.