| Lecturer (assistant) | |
|---|---|
| Duration | 4 SWS |
| Term | Wintersemester 2022/23 |
| Position within curricula | See TUMonline |
| Dates | See TUMonline |
Objectives
The aim of this lecture is to enable the engineer-to-be to describe and understand stress and strain states, material behaviour and limit cases. After the lecture the students can classify several approaches which have been used during their former studies for the description of stress and strain states (e.g. Bernoulli-hypothesis, Timoshenko-beam, plates and shells etc.) according to their limits of application. They can apply different solution procedures and describe stress and strain states in different coordinate systems using tensor calculus. Another goal of the lecture is to empower the students to classify the energy methods and numerical approximation approaches as the Finite Element Method or the Boundary Element Method.
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)