We consider the linearized elasticity equation, discretized with multi-patch Isogeometric Analysis. A standard discretization error analysis is based on Korn's inequality, which degrades for certain geometries, such as long and thin cantilevers. This phenomenon is known as geometry locking. We observe that high-order methods, like Isogeometric Analysis is beneficial in such a setting. The main focus of this paper is the construction and analysis of a domain decomposition solver, namely an Isogeometric Tearing and Interconnecting (IETI) solver, where we prove that the convergence behavior does not depend on the constant of Korn's inequality for the overall domain, but only on the corresponding constants for the individual patches. Moreover, our analysis is explicit in the choice of the spline degree. Numerical experiments are provided which demonstrates the efficiency of the proposed solver.

翻译：本文研究采用多片等几何分析离散的线性化弹性方程。标准离散误差分析基于Korn不等式，该不等式在特定几何构型（如细长悬臂梁）中会退化。该现象称为几何锁死。我们观察到，高阶方法（如等几何分析）在此类情形中具有优势。本文主要工作在于构建并分析一种区域分解求解器——等几何撕裂与互联（IETI）求解器，并证明其收敛性不依赖于整体域的Korn不等式常数，仅取决于各独立片的对应常数。此外，我们的分析显式地依赖于样条次数的选择。数值实验验证了所提求解器的有效性。