After successful completion of the course, students are able to:

• formulate and numerically solve nonlinear partial differential equations for plate and shell problems
• compute extrinsic and intrinsic curvatures with discrete differential geometry and finite elements
• understand which finite elements are suitable for physical and geometric fields

Finite element methods for plates, shells, as well as curvature computations on surfaces and Riemannian manifolds.

Lecture is held on the blackboard / on a Tablet PC in hybrid format.

In the lecture part a balance between mathematical basics of finite elements, discrete differential geometry and applications to shell models and curvature computations on manifolds is attempted. Therefore, numerical simulations of mathematical and physical problems will be incorporated.

In the exercise the theory will be deepened by means of derivations and calculations by hand. In addition, after an introduction to the software NGSolve, numerical experiments on the computer are performed.

The briefing takes place on Tuesday 04.10.22 at 10:00AM in the seminar room DA03 C and parallel online via the Zoom-Link: https://tuwien.zoom.us/j/96551796625?pwd=ZlY0VXdCRllhbHdranl6YUxUQWhOQT09

The Lecture is planed in hybrid format and  the exercise in presence.

Active participation and an oral exam.

A lecture script will be provided via the TUWEL forum. 

• Dietrich Braess: Finite Elemente - Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie
• Dominique Chapelle, Klaus-Jürgen Bathe: The Finite Element Analysis of Shells - Fundamentals
• Manfredo Perdigao do Carmo: Riemannian Geometry
• Michael Neunteufel, 2021: Mixed Finite Element Methods For Nonlinear Continuum Mechanics And Shells, Dissertation, TU Wien

Helpful are basic knowledge of finite element methods. Needed theory of differential geometry will be introduced. The lecture can be adapted to the previous knowledge of the audience.