This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation. It does not increase the bandwidth of the tangent matrix and is effective for both linear and nonlinear problems. It combines isogeometric surface discretizations with classical Lagrange-based surface discretizations, and can thus be run with existing isogeometric finite element codes. Also, the stresses can be recovered straightforwardly. The effectiveness of the proposed approach in alleviating, if not eliminating, membrane locking is demonstrated through the rigorous study of the convergence behavior of several classical benchmark problems. Accuracy gains are particularly large in the membrane stresses. The approach is formulated here for quadratic NURBS, but an extension to other discretization types can be anticipated. The same applies to other constraints and associated locking phenomena.

翻译：本文提出了一种新的混合离散方法，用于缓解基尔霍夫-洛夫壳等几何有限元公式中的薄膜闭锁。该方法简单、无需额外自由度及静力凝聚，不增加切线矩阵带宽，且对线性和非线性问题均有效。它结合了等几何曲面离散与经典拉格朗日曲面离散，因此可直接应用于现有等几何有限元代码，且应力恢复过程简洁。通过若干经典基准问题收敛行为的严格研究，证明了该方法在缓解（甚至消除）薄膜闭锁方面的有效性，尤其在薄膜应力方面精度提升显著。本文针对二次NURBS进行公式推导，但可预见其扩展至其他离散类型，同样适用于其他约束及相关闭锁现象。