This paper proposes an isogeometric formulation of the Reissner–Mindlin shell, using the Mixed Interpolation of Tensorial Components (MITC) technique to alleviate shear locking and membrane locking. Instead of over each Non-Uniform Rational B-Spline (NURBS) element, kinematics of the shell is directly formulated on the entire NURBS patch, with its displacements decoupled to the motions of control points and of director vectors tied to the control points. Since control points are in general not located on the surface, those control-point director vectors are interpolated from normal vectors at a set of pre-defined integration points on the patch. The assumed in-plane membrane strain field and the assumed transverse shear strain field are built as linear combinations of NURBS basis functions with degrees lower than those employed by the displacement interpolation, and tied to the original covariant strain fields at a set of well-selected tying points. Integration points for the definition of control-point director vectors and tying points of the assumed covariant strain fields are provided by the optimal and reduced macro-element quadrature rules, respectively. In this way, the classical MITC technique is fully incorporated into the isogeometric framework with arbitrary polynomial orders or patch configurations. Thanks to the high smoothness of NURBS basis functions, the geometry-preserving nature of isogeometric transformation, and the locking-resistive capability of MITC technique, the isogeometric MITC shell formulation shows superior convergence behavior, minimal geometrical error, and good robustness against patch distortion. In particular, its convergence property is insensitive to NURBS polynomial order or control point density. These advantages are demonstrated through a number of well-established benchmark problems, validating the proposed isogeometric MITC formulation being an accurate and efficient solution for linear analysis of shell structures.

本文提出了Reissner-Mindlin壳的等几何公式，它使用张量分量的混合插值（MITC）技术来减轻剪切锁定和膜锁定。代替在每个非均匀有理B样条（NURBS）元素上覆盖，壳体的运动学直接在整个NURBS面片上制定，其位移与控制点的运动和与控制点相关的导向向量的运动解耦。由于控制点通常不在表面上，因此可以在贴片上的一组预定义积分点处从法向向量内插那些控制点导向向量。假定的面内膜应变场和假定的横向剪应变场构建为NURBS基函数的线性组合，其度数低于位移插值所采用的度数，并与一组精心选择的原始协变应变场相关联捆绑点。定义控制点导向向量的积分点和假定的协变应变场的束缚点分别由最佳和简化的宏单元正交规则提供。通过这种方式，经典的MITC技术已完全结合到具有任意多项式阶数或面片配置的等几何框架中。由于NURBS基函数的高度平滑性，等几何变换的几何保留性质以及MITC技术的抗锁定能力，等几何MITC外壳配方显示出优异的会聚行为，最小的几何误差以及对斑片变形的良好鲁棒性。特别是，其收敛特性对NURBS多项式阶数或控制点密度不敏感。这些优点通过许多公认的基准问题得到了证明，证实了所提出的等几何MITC公式是对壳结构进行线性分析的准确而有效的解决方案。