A discontinuous Galerkin (DG) isogeometric analysis (IGA) formulation with peridynamic (PD) model is proposed for the simulation of cracks in shell structure. A micro-beam PD bond which considers the planar, bending and shearing deformations of shell is applied. Then, based on the micro-beam bond, the peridynamic integral equation is implemented via DG formulation of a conventional isogeometric element. The proposed DGIGA implementation of PD model (DGIGA PD) assures the analysis of crack propagation with spline based smooth geometric model, which is important in the simulation of shell structure. The DGIGA PD calculation improves the computational precision through multiple points based Gaussian integration and provides derivative fields such as strain and stress. To further improve the computational efficiency, the local/nonlocal coupling algorithm for the DGIGA PD model and IGA model is proposed. The computational domain is described fully by spline mesh of IGA, within which the PD domain is assigned where the cracks are propagating. The force and moment balance principal is applied, and an element based stiffness replacing technique is proposed for the coupling process. The performance of the proposed formulation is verified by benchmark examples.

提出了一种具有近场动力学（PD）模型的不连续伽辽金（DG）等几何分析（IGA）公式，用于模拟壳结构中的裂纹。应用了考虑了壳的平面、弯曲和剪切变形的微束 PD 键。然后，基于微束键，通过常规等几何单元的DG公式实现近场动力学积分方程。提出的 PD 模型的 DGIGA 实现 (DGIGA PD) 确保使用基于样条的光滑几何模型分析裂纹扩展，这在壳结构模拟中很重要。DGIGA PD计算通过基于多点的计算提高了计算精度高斯积分并提供衍生场，例如应变和应力。为了进一步提高计算效率，提出了DGIGA PD模型和IGA模型的局部/非局部耦合算法。计算域由 IGA 的样条网格完全描述，其中 PD 域被分配到裂纹传播的位置。应用力和力矩平衡原理，提出了一种基于单元的刚度替换技术用于耦合过程。通过基准示例验证了所提出的公式的性能。