A complete understanding of the wrinkling of compressed films on curved substrates remains illusive due to the limitations of both analytical and current numerical methods. The difficulties arise from the fact that the energetically minimal distribution of deformation localizations is primarily influenced by the inherent nonlinearities and that the deformation patterns on curved surfaces are additionally constrained by the topology. The combination of two factors – the need for dense meshes to mitigate the topological limitations of discretization in domains such as spheres where there is no spherically-symmetric discretizations, and the intensive search for minima in a highly non-convex energy landscape due to nonlinearity – makes existing numerical methods computationally impractical without oversimplifying assumptions to reduce computational costs or introducing artificial parameters to ensure numerical stability. To solve these issues, we have developed a novel (less) reduced version of shell theory for shells subjected to membrane loads, such as during wrinkling. It incorporates the linear contributions of the usually excluded tangential displacements in the membrane strain energy and thus retains the computational efficiency of reduced state-of-the-art methods while nearly achieving the accuracy of the full Kirchhoff–Love shell theory.

中文翻译：

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基于球谐的伪谱方法，用于定量分析软核壳体起皱中的对称性破坏


由于分析和当前数值方法的局限性，完全了解弯曲基板上压缩薄膜的起皱仍然难以理解。困难在于以下事实：变形局域的能量最小分布主要受固有非线性的影响，并且曲面上的变形模式还受到拓扑的约束。两个因素的结合——需要密集网格来减轻在没有球对称离散化的球体等域中离散化的拓扑限制，以及由于非线性而在高度非凸的能量景观中密集寻找最小值——使得现有的数值方法在计算上不切实际，而不会过度简化假设以降低计算成本或引入人工参数来确保数值稳定性。为了解决这些问题，我们开发了一种新的（更少）简化版壳理论，用于承受膜载荷的壳，例如在起皱期间。它结合了膜应变能中通常排除的切向位移的线性贡献，因此保留了简化的最先进方法的计算效率，同时几乎达到了完整的 Kirchhoff-Love 壳理论的准确性。