Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff-Love shells

• Main Authors: Reichle, Mathias, Arf, Jeremias, Simeon, Bernd, Klinkel, Sven
• Format: Journal Article
• Language: English
• Published: 12-04-2023
• Subjects: Computer Science - Numerical Analysis; Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.2304.05857

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.