Analysis Suitability of a Nonlinear Reissner-Mindlin Shell Formulation with Drilling Rotations for Isogeometric Analysis
Analysis Suitability of a Nonlinear Reissner-Mindlin Shell Formulation with Drilling Rotations for Isogeometric Analysis
"Analysis Suitability of a Nonlinear Reissner-Mindlin Shell Formulation with Drilling Rotations for Isogeometric Analysis", organizado por CITMAga. Será impartido por Jeremias Arf. Dept. of Mathematics, RPTU Kaiserslautern-Landau (Germany).
Data: 18 de xullo de 2025.
Hora: 10:00 h.
Duración: 1 hora
Lugar: Salón de Graos da Facultade de Matemáticas (USC) e en liña por MS Teams a través do enlace Teams Meeting.
Abstract:
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 scaled-boundary 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.
[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.