all lectures

Basic data

Prüfung schriftlich 60 Minuten.

Parallel groups / dates

- Statische Probleme: Belastung der Muskeln und Gelenke
- Elastostatische Probleme: Belastung der Knochen
- Grundlagen der linearen FEM: Ermittlung von Verschiebung, Dehnung und Spannung
- Elastizität der Blutgefäße
- Biomaterialverhalten: Viskoelastizität und Plastizität

Basic data

Parallel groups / dates

- Force and Moment, Axioms of Statics
- planar and stereo Statics
- Static Moment, Moment of Inertia
- Tribology
- Work
- Stress, Deformation, Constitutive Equations
- overdetermined Frameworks, Beam Bending
- Torsion
- Energy Methods in Elastostatics
- Stability
- Theory of Elasticity and Strength of Material null

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

In this course, numerical methods that preserve the geometric properties of the flow of a differential equation will be presented and analysed.

Basic concepts on numerical integration theory such as consistency and convergence will be introduced. Several numerical integration methods, such as Runge-Kutta, collocation, partitioned methods, composition and splitting methods, will be introduced. The concept of first integrals and conditions for their preservation by some of these methods will be derived and proven.

We will be particularly concerned with the numerical integration of Lagrangian and Hamiltonian systems, which will lead to the introduction of symplectic methods. Basic concepts such as Hamilton's principle, symplecticity, and Noether's theorem will be introduced. It will be shown how a discrete formulation of these principles leads to a class of integrators known as variational integrators which are equivalent to the class of symplectic methods. We will prove why symplectic methods lead to more accurate long-time integration by introducing the concept of backward error analysis.

The theoretical introduction of these topics will be accompanied by analytical and practical exercises to consolidate these ideas. Some of the tasks will involve the implementation of code in Python to run simulations. An introduction to Python and some of the necessary packages will also be contained as part of the sessions. null

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates

Basic data

Parallel groups / dates