Continuum Mechanics and Tensor Calculus

Lecturer:

Dr.-Ing. Rainer Schlebusch, Dr.-Ing. Mike Richter 

Qualification aims:

The students master the applied tensor calculus and know the basics of continuum mechanics. The students have an overview of the central topics, work and application fields of continuum mechanics and tensor calculus.

Contents:

Contents of the module are topics on linear algebra, tensor algebra and analysis as well as topics on the basics of continuum mechanics. Topics covered include vector calculus, matrix algebra, vector spaces with and without an inner product, normalized spaces, linear mappings/tensors, products of tensors, eigenvalue problems, tensor-valued tensor functions and their derivatives, tensor fields and differential operators, and the kinematics of deformations, stress tensors, conservation and balance equations, and elastic material models.

Type of course:

4 hours of lectures, 2 hours of exercises per week, and self-study.

Requirements for study:

Basic knowledge in the fields of linear algebra and multidimensional analysis as well as knowledge of engineering mechanics, especially in the fields of linear elasticity theory and strength of materials theory at the bachelor's level are required.

Practical use of the module:

The module is a compulsory module in the Master's programme Advanced Computational and Civil Engineering Structural Studies - ACCESS. It provides the prerequisites for the modules Form Finding of Lightweight Structures, Constitutive Modelling of Soils, Multiscale Mechanics and Numerical Dynamics.

Requirements for the award of academic credits:

The credit points are awarded if the module examination is successfully passed. The module examination consists of a written exam of 90 minutes and an ungraded portfolio of 60 hours. The examination language is English.

Remarks:

At the Department of Civil Engineering we employ two different systems of grading. Most modules are completed with an (oral or written) exam or a graded essay, paper, or thesis and these will be graded on a scale from excellent (1.0) to fail (5). This is then the grade for the module.

However, this module will be completed first by an portfolio graded only passed or failed, and second by a written examination graded on a scale from 1.0 to 5.

Credits and grades:

Eight credit points can be acquired for this module. The module grade results from the weighted average of the grades of the written exam and the portfolio, taking into account § 15 paragraph 1 clauses 5 and 6 of the examination regulations. The written exam is weighted twice and the portfolio is weighted once.

Remarks:

If the portfolio is passed the grade of the written examination is the grade of the module. The assignment has not further influence on the final grade for the module.

The failing grade for the portfolio is 5 and the grade of the module is calculated from the weighted arithmetic average (see table below).

assignment (non-graded)	grade of written exam	grade of module
failed	1.0	2.3
failed	1.3	2.5
failed	1.7	2.8
failed	2.0	3.0
failed	2.3	3.2
failed	2.7	3.4
failed	3.0	3.6
failed	3.3	3.8
failed	3.7	5
failed	4	5

 

Frequency of module offering:

The module is offered every academic year in winter semester.

Workload:

The total workload is 240 hours.

Duration of the module:

The module lasts one semester.