Isogeometric MITC shell
Isogeometric MITC shell
复制标题
等几何 MITC 壳
DOI：
10.1016/j.cma.2021.113693
复制
发表时间：
2021
影响因子：
7.2
通讯作者：
Xiang Yu
中科院分区：
文献类型：
--
作者：
Yongzhen Mi;Xiang Yu
本文提出了一种Reissner-Mindlin壳的等几何公式，该公式采用张量分量混合插值（MITC）技术来减轻剪切锁紧和膜锁紧。而不是在每个非均匀有理b样条（NURBS）元素上，壳的运动学直接在整个NURBS补丁上制定，其位移解耦到控制点的运动和指向向量绑定到控制点。由于控制点通常不位于表面上，这些控制点方向向量是从补丁上一组预定义积分点的法向量插值而来的。假设的平面内膜应变场和假设的横向剪切应变场被构建为低于位移插值所使用的NURBS基函数的线性组合，并在一组精心选择的绑扎点上与原始协变应变场绑定。定义控制点方向向量的积分点和假设共变应变场的结合点分别由最优宏元正交规则和简化宏元正交规则提供。这样，经典的MITC技术就完全融入了具有任意多项式阶或贴片构型的等几何框架中。由于NURBS基函数的高平滑性、等几何变换的几何保持性以及MITC技术的抗锁定能力，等几何MITC壳公式具有优异的收敛性、最小的几何误差和良好的抗贴片畸变鲁棒性。其收敛性对NURBS多项式阶数和控制点密度不敏感。这些优点通过一系列成熟的基准问题得到了证明，验证了所提出的等几何MITC公式是壳结构线性分析的准确和有效的解决方案。
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.
DOI：
10.1016/j.cma.2009.08.013
发表时间：
2009-01-01
影响因子：
7.2
作者：
Kiendl, J.;Bletzinger, K-U.;Wuechner, R.
通讯作者：
Wuechner, R.
DOI：
10.1016/j.cma.2019.05.037
发表时间：
2019-09
影响因子：
7.2
作者：
G. Kikis;W. Dornisch;S. Klinkel-
通讯作者：
G. Kikis;W. Dornisch;S. Klinkel-
DOI：
10.1016/j.cma.2012.10.018
发表时间：
2013-02-01
影响因子：
7.2
作者：
Echter, R.;Oesterle, B.;Bischoff, M.
通讯作者：
Bischoff, M.