Four nonlinear computational models for the surface wrinkling of curved shell-core systems under external pressure are presented. Three of the considered finite element models neglect the displacements tangential to the shell surface. Two of the models are static formulations and the other two are derived in the dynamic framework. For the latter, the energy-decaying time-stepping algorithm is applied, which is suitable for numerically stiff problems, such as shell-core systems, characterized by stiff membrane and soft wrinkling deformation modes. In all cases the core is modeled by elastic springs. As a comparative problem we choose the surface wrinkling of pressurized shell-core spheres. In particular, five systems with different material and geometric properties are computed, which have different wrinkle patterns. A good agreement is found between the results of the models as well as with the relevant references, which provide numerical and experimental results. However, it has been observed that our reduced-order models are blind to the prediction of the secondary transformation – from the dimple-like pattern to the labyrinthine pattern. Another conclusion is that a non-tailored (i.e. standard) shell finite element on an elastic foundation combined with the energy-decaying scheme, provides excellent predictions of the surface wrinkle patterns.

提出了在外部压力下弯曲壳核系统表面起皱的四个非线性计算模型。所考虑的有限元模型中的三个忽略了与壳表面相切的位移。其中两个模型是静态公式，另外两个是在动态框架中派生的。对于后者，应用了能量衰减的时间步长算法，该算法适用于数值刚性问题，例如以刚性膜和软起皱变形模式为特征的壳核系统。在所有情况下，芯子都是通过弹性弹簧建模的。作为一个比较问题，我们选择加压壳核球的表面起皱。特别是，计算了五个具有不同材料和几何特性的系统，它们具有不同的皱纹模式。在模型的结果以及与相关参考文献之间可以找到很好的一致性，这些参考文献提供了数值和实验结果。但是，已经观察到，我们的降阶模型对二次转化的预测是盲目的-从酒窝状模式到迷宫式模式。另一个结论是，弹性基础上的非定制（即标准）壳有限元与能量衰减方案相结合，可提供表面皱纹模式的出色预测。