A Geometrically Nonlinear Reissner-Mindlin Shell with Load‑Step‑Driven Mesh Adaptation

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

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Beyond the analysis-suitability of a shell model, meaning its applicability to a wide range of scenarios, such as shells with kinks, stiffeners, or thin and moderately thick structures, there is a second aspect that is crucial for practical use: adaptive mesh refinement. This capability allows a significant reduction in the number of degrees of freedom ([1]), especially in situations involving spatially concentrated forces and moments or regions of strong local deformation, both of which occur frequently in real-world applications. To address all these requirements, we build upon a Reissner–Mindlin shell formulation enriched with an additional drilling degree of freedom ([2]). The model is geometrically nonlinear, and the introduction of a dedicated drilling stiffness ensures that the geometric description and underlying approximation spaces require only C0-regularity, an important advantage for usability. In addition, we employ a vector-like parametrization of finite rotations. This approach enables us to express all relevant quantities as functions parametrized consistently over the entire shell surface, while supporting an additive update of both, displacements and rotations. As a result, mesh-refinement steps can be performed seamlessly, and all quantities at new quadrature points can be evaluated exactly without any need for averaging or interpolation. The discretization follows the isogeometric analysis (IGA) paradigm and exploits THB-splines ([3]), enabling us to combine exact geometric representation with fully local mesh refinement possibilities. We propose performing load-step-driven refinement, introducing new mesh elements in regions exhibiting increased strain values. Through a range of numerical examples, including smooth surfaces and shells with kinks, we demonstrate the suitability of the approach for integrating adaptive multi-patch IGA with geometrically nonlinear shell formulations. REFERENCES [1] C. Bracco, A. Farahat, C. Giannelli, M. Kapl, R. Vázquez, Adaptive methods with C1 splines for multi-patch surfaces and shells, CMAME, Vol. 431, 2024. [2] A. Ibrahimbegović, Stress resultant geometrically nonlinear shell theory with drilling rotations–Part I. A consistent formulation, CMAME, Vol. 118, 1994. [3] C. Giannelli, B. Jüttler, S. K. Kleiss, A. Mantzaflaris, B. Simeon, J. Špeh, THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis, CMAME, Vol. 299, 2016.