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Conferenciante: Jeremias Arf. Department of Mathematics, RPTU Kaiserslautern-Landau (Alemania)
Resumo:
Shell analysis of thin structures is of great importance in modern engineering fields like aerospace and structural
mechanics. A key challenge lies in transferring data from Computer Aided Design (CAD) to analysis models without loss
of properties. Shell theories such as Kirchhoff-Love [1] and Reissner-Mindlin offer modeling foundations, with the latter
accommodating transverse shear deformation and thus being suitable for thick shells. We present a geometrically
nonlinear shell formulation based on the Reissner-Mindlin approach, incorporating deformation and three rotation
variables. By including drilling stabilization, the method requires only C0 continuity in both the geometry and finite
element spaces. Unlike classical approaches such as Kirchhoff-Love, this allows the direct modeling of structures with
kinks-no preprocessing needed. Furthermore, the formulation's low regularity demands facilitate integration with scaledboundary
parametrizations or local refinement methods using hierarchical E-splines [2], enhancing flexibility in mesh
and geometry design. The model is discretized via Isogeometric Analysis (IGA) [3], enabling exact representation of
curved surfaces and efficient use of degrees of freedom through krefinement.
Performance and analysis suitability are
validated through benchmark tests using our implementation in the GeoPDEs framework.
Referencias
[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] C. Giannelli, B. Jüttler, S. K. Kleiss, A. Mantzaflaris, B. Simeon, J. Speh, THB-splines: An effective mathematical technology
for adaptive refinement in geometric design and isogeometric analysis, Comput. Meth. Appl. Mech. Eng., Vol. 299, 2016.
[3] M.-J. Choi, Isogeometric Configuration Design Sensitivity Analysis of Geometrically Exact Nonlinear Structures. Doctoral
dissertation, Seoul National University, 2019.