具有各向异性生长的细分壳单元
Subdivision Shell Elements with Anisotropic Growth
AI总结：
提出一种基于Loop细分曲面的薄壳有限元方法，用于处理大变形和各向异性生长，通过数值模拟展示其广泛应用。
摘要：
提出了一种基于Loop细分曲面的薄壳有限元方法，能够处理大变形和各向异性生长。为此，推导了Kirchhoff-Love薄壳理论并扩展以允许任意面内生长。细分壳单元的简单性和计算效率非常突出，这在几个标准加载基准测试中得到了证明。借助这一强大工具，我们通过数值求解多个生长场景（从球体的均匀生长到由大各向异性生长引起的边界不稳定性）展示了广泛的应用范围。最后，证明了在固定空心球内缓慢均匀生长的薄片问题等价于在无摩擦、准静态、弹性极限下，固定尺寸的薄片在收缩空心球内缓慢皱缩的逆过程。
英文摘要：
A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.
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