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 classical $$\bar{B}$$ B ¯ method. 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 $$10^5$$ 10 5 , 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.

中文翻译：

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薄 Reissner-Mindlin 壳的等几何分析：锁定现象和 B 杆法

我们提出了一种局部类型的 B-bar 公式，解决了等几何分析背景下退化 Reissner-Mindlin 壳公式中的锁定问题。使用最小二乘法将寄生应变分量局部投影到物理空间，即在单元级。该公式允许灵活利用不同阶的基函数作为投影基。引入的公式在计算上比经典的 $$\bar{B}$$ B¯ 方法便宜得多。我们通过数值例子展示了该方案的数值一致性，此外，它们表明，即使对于 $$10^5$$$10 5 的细长比，所提出的公式也能减轻锁定并产生良好的精度，并且能够使用相对粗糙的网格。