IGA2025

Nonlinear Reissner-Mindlin Shell Formulation for block-wise Scaled Boundary Parametrizations

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

Please login to view abstract download link

In the recent years, the amenities of IGA have been successfully leveraged in various field of continuum mechanics, for example in the context of shell theory, as shells appear in different application scenarios. In particular, the Kirchhoff-Love model (KLM), a displacement based formulation which requires C1 smooth basis functions, has already been discussed [1] and implemented, even in a multi-patch setting. However, we want to address the Reissner-Mindlin shell formulation that incorporates rotation variables alongside the deformation. This enables the realistic modeling also of thick shells since it accounts for shear deformations, whereas the KLM is restricted to thin structures; see [2]. Thereby, it is possible to generalize to C0 regular ansatz functions and parametrizations which simplifies implementation and increases flexibility. On the one hand, in view of the latter, we build on a specific parametrization paradigm, namely the Scaled boundary IGA [3]. More precisely, we divide our domain in multiple blocks, which we discretize utilizing a scaling with respect to a well-chosen scaling center. Using, this we can represent easily complicated shapes and after a proper update of the boundary curves, it is achievable to integrate trimming curves in an exact manner. On the other hand, we allow geometric non-linearities, hence, large deformations are feasible. Our investigations will be demonstrated by means of different numerical examples and we review to what extent we obtain a competitive new shell implementation. [1] C. Bracco, A. Farahat, C. Giannelli, M. Kapl, R. Vázquez, Adaptive methods with C1 splines for multi-patch surfaces and shells, Computer Methods in Applied Mechanics and Engineering (2024) 431. [2] W. Dornisch, S. Klinkel, B. Simeon, Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors, Computer Methods in Applied Mechanics and Engi- neering (2013) 253. [3] J. Arf, M. Reichle, S. Klinkel, B. Simeon, Scaled boundary isogeometric analysis with C1 coupling for Kirchhoff plate theory, Computer Methods in Applied Mechanics and Engineering (2023) 415.