An Analysis-Suitable Reissner-Mindlin Shell Formulation for Polygonal Scaled Boundary Isogeometric Analysis

  • Reichle, Mathias (RWTH Aachen University)
  • Arf, Jeremias (RPTU Kaiserslautern-Landau)
  • Choi, Myung-Jin (RWTH Aachen University)
  • Simeon, Bernd (RPTU Kaiserslautern-Landau)
  • Klinkel, Sven (RWTH Aachen University)

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A crucial aspect of structural analysis is the direct transfer of the computational design to the engineering analysis. For shell structures, it is particularly beneficial to consider smooth transitions, kinks, and stiffeners without relying on additional assumptions at intersections. Besides geometrical features, the underlying representation is often not straight-forwardly transferable to the analysis model due to modifications such as trimming or boundary representations. In this contribution, the scaled boundary isogeometric analysis is utilized as surface discretization [1]. It is a boundary-oriented approach that is especially suitable to handle complex domains and trimmed shapes. Further, an isogeometric shell formulation based on the Reissner–Mindlin assumptions is presented enhanced by incorporating a drilling degree of freedom. This extension eliminates the need to distinguish between smooth transitions and kinks [2, 3]. As a result, the scaled boundary parametrization can be applied directly without preprocessing across patch interfaces — an important feature in view of realistic multi-patch surfaces. Additionally, the inclusion of drilling stiffness relaxes the continuity requirements such that a C0 parametrization across patches suffices. Several example including geometric nonlinearity demonstrate the applicability of the proposed approach to various tesselation techniques. The advantages of combining scaled boundary isogeometric analysis and conventional isogeometric analysis in hybrid parametrizations are highlighted. Summarized, an analysis-suitable framework is presented for Reissner–Mindlin shell analysis of complex and trimmed design models in a seamless pipeline from design to analysis. REFERENCES [1] M. Reichle, J. Arf, B. Simeon and S. Klinkel, Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff–Love shells. Meccanica, Vol. 58, pp. 1693–1716, 2023. [2] M.-J. Choi, Isogeometric Configuration Design Sensitivity Analysis of Geometrically Exact Nonlinear Structures. Doctoral dissertation, Seoul National University, 2019. [3] A. Ibrahimbegovíc, Stress resultant geometrically nonlinear shell theory with drilling rotations — Part I. A consistent formulation. Comput. Meth. Appl. Mech. Eng., Vol. 118, pp. 265–284, 1994.