The objective of this article is to simulate crack growth of complex Mindlin–Reissner plates by developing an adaptive multi-patch extended isogeometric analysis (XIGA). Nitsche’s method is used to treat continuity between multi-patches or the coupling of non-conforming meshes, exactly describing the geometry of complex plates. The computational meshes in XIGA are independent of the cracks by introducing some enrichment functions into the displacement approximation based on the partition of unity, thus it is convenient in modeling evolution of crack. The locally refined non-uniform rational B-splines (LR NURBS), which have the properties of local refinement and exact description of geometry, are used to construct geometric model and taken as the shape functions in XIGA. To implement the adaptive local refinement, a method based on recovery technique by Zienkiewicz and Zhu is proposed. Based on the Mindlin–Reissner plate theory, interaction integral method is employed to calculate stress intensity factors (SIFs) and the maximum circumferential stress criterion is used to determine the crack propagation direction. Several numerical examples are carried out to demonstrate the performance of the adaptive multi-patch XIGA for simulating crack growth in complex plates.

本文的目的是通过开发自适应多面体扩展等几何分析（XIGA）来模拟复杂Mindlin-Reissner板的裂纹扩展。Nitsche的方法用于处理多面体之间的连续性或不合格网格的耦合，准确地描述了复杂板的几何形状。XIGA中的计算网格通过将一些富集函数引入基于单位分配的位移近似中而与裂纹无关，从而便于对裂纹的演化进行建模。具有局部细化特性和对几何的精确描述的局部细化非均匀有理B样条（LR NURBS）被用于构建几何模型并作为XIGA中的形状函数。要实施自适应局部优化，提出了一种基于Zienkiewicz和Zhu的恢复技术的方法。根据Mindlin-Reissner板理论，采用相互作用积分法计算应力强度因子（SIF），并使用最大周向应力准则确定裂纹扩展方向。进行了几个数值示例，以证明自适应多面体XIGA在模拟复杂板中裂纹扩展方面的性能。