In order to model prominent failure modes experienced by multi-layered composites, a fine through-thickness discretisation is needed. If the structure also has large in-plane dimensions, the computational cost of the model becomes large. In light of this, we propose an adaptive isogeometric continuum shell element for the analysis of multi-layered structures. The key is a flexible and efficient method for controlling the continuity of the out-of-plane approximation, such that fine detail is only applied in areas of the structure where it is required. We demonstrate how so-called knot insertion can be utilised to automatise an adaptive refinement of the shell model at arbitrary interfaces, thereby making it possible to model multiple initiation and growth of delaminations. Furthermore, we also demonstrate that the higher-order continuity of the spline-based approximations allows for an accurate recovery of transverse stresses on the element level, even for doubly-curved laminates under general load. With this stress recovery method, critical areas of the simulated structures can be identified, and new refinements (cracks) can be introduced accordingly. In a concluding numerical example of a cantilever beam with two initial cracks, we demonstrate that the results obtained with the adaptive isogeometric shell element show good correlation with experimental data.

为了模拟多层复合材料所经历的显着失效模式，需要精细的全厚度离散化。如果结构也具有较大的平面内尺寸，则模型的计算成本会变大。鉴于此，我们提出了一种用于多层结构分析的自适应等几何连续体壳单元。关键是一种灵活有效的方法来控制平面外近似的连续性，这样精细的细节只应用于需要它的结构区域。我们展示了如何利用所谓的结插入来自动化任意界面上壳模型的自适应细化，从而可以对分层的多次启动和增长进行建模。此外，我们还证明了基于样条的近似值的高阶连续性允许在单元水平上准确恢复横向应力，即使对于一般载荷下的双弯曲层压板也是如此。使用这种应力恢复方法，可以识别模拟结构的关键区域，并可以相应地引入新的改进（裂缝）。在具有两个初始裂纹的悬臂梁的结论性数值示例中，我们证明了使用自适应等几何壳单元获得的结果与实验数据具有良好的相关性。并且可以相应地引入新的改进（裂缝）。在具有两个初始裂纹的悬臂梁的结论性数值示例中，我们证明了使用自适应等几何壳单元获得的结果与实验数据具有良好的相关性。并且可以相应地引入新的改进（裂缝）。在具有两个初始裂纹的悬臂梁的结论性数值示例中，我们证明了使用自适应等几何壳单元获得的结果与实验数据具有良好的相关性。