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

Meccanica, vol. 58, pp. 1693–1716

Abstract

Abstract 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 $$C^1$$ C 1 -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 $$G^1$$ G 1 parametrizations. This yields a coupling of patch boundaries in a strong sense that is restricted to $$G^1$$ G 1 -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. Since the coupling of star-shaped blocks is feasible, a mesh generation also for complex domains is implementable. 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.

Authors 4

1. Mathias Reichle corresponding Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Aachen, Germany

2. Jeremias Nathanael Arf

   University of Kaiserslautern · Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

   Affiliation as printed

   Department of Mathematics, RPTU Kaiserslautern-Landau, Kaiserslautern, Germany

3. Bernd Simeon

   University of Kaiserslautern · Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

   Affiliation as printed

   Department of Mathematics, RPTU Kaiserslautern-Landau, Kaiserslautern, Germany

4. Sven Klinkel Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Aachen, Germany