We introduce an adaptive isogeometric method for multi-patch surfaces and Kirchhoff–Love shell structures with hierarchical splines characterized by C1 continuity across patches. We extend the construction of smooth hierarchical splines from the multi-patch planar setting to analysis suitable G1 surfaces. The adaptive scheme to solve fourth order partial differential equations is presented in a general framework before showing its application for the numerical solution of the bilaplacian and the Kirchhoff–Love model problems. A selection of numerical examples illustrates the performance of hierarchical adaptivity on different multi-patch surface configurations.

中文翻译：

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使用 [公式省略] 样条曲线的自适应方法，用于多面片曲面和壳


我们引入了一种自适应等几何方法，用于多面片表面和 Kirchhoff-Love 壳结构，其分层样条的特点是跨面片的 C1 连续性。我们将平滑分层样条的构造从多面片平面设置扩展到分析合适的 G1 曲面。在展示其在 bilaplacian 和 Kirchhoff-Love 模型问题的数值解中的应用之前，在一般框架中介绍了求解四阶偏微分方程的自适应方案。一系列数值示例说明了分层自适应性在不同多面片曲面配置上的性能。