Speaker
Description
The numerical treatment of Kirchhoff–Love shells is challenging due to fourth-order derivatives in the displacement-based strong form of the governing mechanical model. For the finite element analysis, the employed shape functions must either meet increased continuity requirements such as those provided in isogeometric analysis or—to continue using standard C0‑continuous elements—mixed formulations are needed. Then, the components of the displacement vector and the moment tensor are typically present as primary variables, largely increasing the number of unknowns. A hybridized formulation, see [1], may address this disadvantage, where an element-wise static condensation reduces the number of overall DOFs, leading only to displacements and rotations on element boundaries as the resulting primary variables. The moment tensor may be retrieved in a post-processing step with improved convergence rates compared to the moment tensor computed in a displacement-based formulation. We present a novel mixed-hybrid finite element approach, where classical C0‑continuous shape functions based on higher-order Lagrange elements are employed without the need for special finite element spaces such as in [2]. All mechanically useful boundary conditions are systematically considered. The weak form is formulated in the frame of the tangential differential calculus (TDC) following our works in [3, 4, 5], thus being applicable to explicitly and implicitly defined shell geometries. A new set of benchmark test cases featuring smooth mechanical fields is proposed, where the numerical results confirm optimal higher-order convergence rates.
REFERENCES
[1] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications, 1 ed., Springer-Verlag Berlin Heidelberg, Berlin, 2013.
[2] M. Neunteufel, J. Schöberl, The Hellan–Herrmann–Johnson method for nonlinear shells, Comput. Struct., 225, 106109, 2019.
[3] D. Schöllhammer, T.-P. Fries, Kirchhoff–Love shell theory based on tangential differential calculus, Comput. Mech., 64, 113–131, 2019.
[4] D. Schöllhammer, T.-P. Fries, Reissner–Mindlin shell theory based on tangential differential calculus, Comput. Method. Appl. M., 352, 172–188, 2019.
[5] D. Schöllhammer, T.-P. Fries, A higher‐order Trace finite element method for shells, Int. J. Numer. Meth. Eng., 122, 1217–1238, 2021.
