Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method
Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method
复制标题
Reissner-Mindlin 薄壳的等几何分析：锁定现象和 B 杆方法
DOI：
10.1007/s00466-020-01821-5
复制
发表时间：
2020
影响因子：
4.1
通讯作者：
Bordas Stephane P. A.
中科院分区：
文献类型：
--
作者：
Hu Qingyuan;Xia Yang;Natarajan Sundararajan;Zilian Andreas;Hu Ping;Bordas Stephane P. A.
我们提出了一个本地类型的B-酒吧制定，解决锁定退化Reissner-Mindlin壳制定的上下文中的等几何分析。寄生应变分量被投影到物理空间的本地，即在元素级，使用最小二乘法。该公式允许灵活地利用不同阶的基函数作为投影基。所引入的公式比经典方法计算量小得多。我们通过数值算例表明了该格式的数值一致性，并且表明该格式即使在细长比为的情况下也能消除锁定并产生良好的精度，并且能够使用相对粗糙的网格捕获薄壳的变形。此外，可以认为所提出的方法对不规则网格的锁定不太敏感。
We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation allows the flexible utilization of basis functions of different orders as the projection bases. The introduced formulation is much cheaper computationally than the classicalmethod. We show the numerical consistency of the scheme through numerical examples, moreover they show that the proposed formulation alleviates locking and yields good accuracy even for slenderness ratios of, and has the ability to capture deformations of thin shells using relatively coarse meshes. In addition it can be opined that the proposed method is less sensitive to locking with irregular meshes.