# 101.974 AKNUM Finite Elements for Differential Geometry This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2022W

2022W, VU, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VU Lecture and Exercise
• Format: Hybrid

## Learning outcomes

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

## Subject of course

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

## Teaching methods

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.

## Mode of examination

Immanent

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.

## Course dates

DayTimeDateLocationDescription
Tue10:00 - 12:0004.10.2022 - 24.01.2023 Seminarraum DA03 CLecture
Tue10:00 - 12:0004.10.2022 Seminarraum DA03 CBriefing
Thu14:00 - 15:0006.10.2022 - 24.11.2022Sem.R. DA grün 02 C Exercise
Thu15:00 - 16:0020.10.2022Sem.R. DA grün 06B Exercise
Thu14:00 - 16:0024.11.2022 - 26.01.2023Sem.R. DA grün 06B lecture/Exercise
AKNUM Finite Elements for Differential Geometry - Single appointments
DayDateTimeLocationDescription
Tue04.10.202210:00 - 12:00 Seminarraum DA03 CLecture
Tue04.10.202210:00 - 12:00 Seminarraum DA03 CBriefing
Thu06.10.202214:00 - 15:00Sem.R. DA grün 02 C Exercise
Tue11.10.202210:00 - 12:00 Seminarraum DA03 CLecture
Thu13.10.202214:00 - 15:00Sem.R. DA grün 02 C Exercise
Tue18.10.202210:00 - 12:00 Seminarraum DA03 CLecture
Thu20.10.202215:00 - 16:00Sem.R. DA grün 06B Exercise
Tue25.10.202210:00 - 12:00 Seminarraum DA03 CLecture
Thu27.10.202214:00 - 15:00Sem.R. DA grün 02 C Exercise
Thu03.11.202214:00 - 15:00Sem.R. DA grün 02 C Exercise
Tue08.11.202210:00 - 12:00 Seminarraum DA03 CLecture
Thu10.11.202214:00 - 15:00Sem.R. DA grün 02 C Exercise
Thu17.11.202214:00 - 15:00Sem.R. DA grün 02 C Exercise
Tue22.11.202210:00 - 12:00 Seminarraum DA03 CLecture
Thu24.11.202214:00 - 15:00Sem.R. DA grün 02 C Exercise
Thu24.11.202214:00 - 16:00Sem.R. DA grün 06B lecture/Exercise
Tue29.11.202210:00 - 12:00 Seminarraum DA03 CLecture
Thu01.12.202214:00 - 16:00Sem.R. DA grün 06B lecture/Exercise
Tue06.12.202210:00 - 12:00 Seminarraum DA03 CLecture
Tue13.12.202210:00 - 12:00 Seminarraum DA03 CLecture

## Examination modalities

Active participation and an oral exam.

## Course registration

Begin End Deregistration end
01.09.2022 00:00 12.10.2022 23:59 31.10.2022 23:59

## Literature

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

## Previous knowledge

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.

## Language

if required in English