In this work, a linear Kirchhoff-Love shell formulation in the framework of scaled boundary isogeometric analysis is presented that aims to provide a simple approach to trimming for NURBS-based shell analysis. To obtain a global C1-regular test function space for the shell discretization, an inter-patch coupling is applied with adjusted basis functions in the vicinity of the scaling center to ensure the approximation ability. Doing so, the scaled boundary geometries are related to the concept of analysis-suitable G1 parametrizations. This yields a coupling of patch boundaries in a strong sense that is restricted to G1-smooth surfaces. The proposed approach is advantageous to trimmed geometries due to the incorporation of the trimming curve in the boundary representation that provides an exact representation in the planar domain. The potential of the approach is demonstrated by several problems of untrimmed and trimmed geometries of Kirchhoff-Love shell analysis evaluated against error norms and displacements. Lastly, the applicability is highlighted in the analysis of a violin structure including arbitrarily shaped patches.

翻译：本文提出了基于缩放边界等几何分析框架的线性Kirchhoff-Love壳体公式，旨在为基于NURBS的壳体分析提供一种简化的剪裁处理方法。为获得全局C1正则试探函数空间以离散壳体，采用相邻补片耦合策略，通过调整缩放中心附近基函数保持逼近能力。由此，缩放边界几何与分析适用G1参数化概念相关联，实现了补片边界在强意义下的耦合，并局限于G1光滑曲面。该方法因将剪裁曲线直接嵌入边界表示中，可在平面域提供精确表示，从而对剪裁几何具有优势。通过Kirchhoff-Love壳体分析中非剪裁与剪裁几何的多个数值算例，基于误差范数与位移验证了该方法的潜力。最后，通过包含任意形状补片的小提琴结构分析，进一步凸显其适用性。