| Lecturer (assistant) | |
|---|---|
| Duration | 4 SWS |
| Term | Winter semester 2025/26 |
| Position within curricula | See TUMonline |
| Dates | See TUMonline |
Description
The lecture Continuum Mechanics deals with the analytical and numerical solution procedures for the general three-dimensional continuum under static and time-variant loads.
Continuum mechanics enables the students to understand more-dimensional stress and strain states. It is the basis for static and dynamic analysis of two-dimensional structures and three-dimensional continua (e.g. the soil). Numerical computational methodologies as the Finite Element Method, the Boundary Element Method or the Statistical Energy Analysis are resting on continuum mechanics.
For certain constellations also analytical solutions for the structural response of systems and fundamental coherences (e.g. resonance phenomena, wave propagation) can be demonstrated with continuum mechanical approaches. An understanding of continuum mechanical interrelations and their solutions enables the engineer to control the results of numerical computations by plausibility checks.
An important auxiliary mean for the description of continuum mechanical questions is tensor analysis. It is presented during the lectured in index notation with references to symbolic notation.
Thematic outline:
- Introduction into tensor analysis
- Description of stress states in arbitrary, curvilinear coordinates
- Lagrangian description of strain states
- Conservation of energy
- Conservation of mass
- Constitutive relations
- General treatment of continuum mechanical knowledge in order to solve non-linear problems
- References to approaches of Technical Mechanics (Torsion, Bending, Plates, Dynamics)
Continuum mechanics enables the students to understand more-dimensional stress and strain states. It is the basis for static and dynamic analysis of two-dimensional structures and three-dimensional continua (e.g. the soil). Numerical computational methodologies as the Finite Element Method, the Boundary Element Method or the Statistical Energy Analysis are resting on continuum mechanics.
For certain constellations also analytical solutions for the structural response of systems and fundamental coherences (e.g. resonance phenomena, wave propagation) can be demonstrated with continuum mechanical approaches. An understanding of continuum mechanical interrelations and their solutions enables the engineer to control the results of numerical computations by plausibility checks.
An important auxiliary mean for the description of continuum mechanical questions is tensor analysis. It is presented during the lectured in index notation with references to symbolic notation.
Thematic outline:
- Introduction into tensor analysis
- Description of stress states in arbitrary, curvilinear coordinates
- Lagrangian description of strain states
- Conservation of energy
- Conservation of mass
- Constitutive relations
- General treatment of continuum mechanical knowledge in order to solve non-linear problems
- References to approaches of Technical Mechanics (Torsion, Bending, Plates, Dynamics)