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2023S, UE, 2.0h, 2.0EC

## Properties

• Semester hours: 2.0
• Credits: 2.0
• Type: UE Exercise
• Format: Distance Learning

## Learning outcomes

After successful completion of the course, students are able to

• solve theoretical problems regarding continuum mechanics of solid bodies by means of mathematical foundations (tensor algebra and analysis)
• apply various strain measures to practical problems and know how to use them properly
• apply displacment-strain relations for large deformations
• compute strains for a given displacement field
• apply various stress measures to practical problems and know how to use them properly
• compute the stresses in a body as a consequence of the external loading by means of balance equations
• apply simple constitutive laws (incompressible hyperelastic isotropic materials) to practical problems
• differentiate between plane stress and plane strain assumptions

## Subject of course

Application of theory of continuum mechanics of solid bodies (see VO) on practical problems.

The content of the exercise is split into 7 subchapters:

1) Mathematical foundations

• Linear algebra (only repitition, basics are required, e.g. as matrix multiplications, calculation of the determinante, calculation of the inverse of a matrix, solving an eigenvalue problem etc.)
• Tensor algebra
• Tensor analysis
• Transformation of coordinates

2) Kinematics of continuum I

• Motion, velocity and acceleration in material and spatial description

3) Kinematics of continuum II

• Stretch tensors, strain tensors, principal stretch tensor etc.

4) Kinetics of continuum

• Traction vectors, stress tensors, principal stress tensors, axes of principal stresses etc.

5) Balance principles

• Conservation of mass and principle of linear momentum

6) Constitutive equations

• Influence of linearization on constitutive equations
• Incompressible hyperelastic isotropic materials

7) Plane stress and plane strain

• Elasticity matrices for plane stress and plane strain

## Teaching methods

In the style of an "Inverted Classroom". Examples are presented. A short review of the necessary theory (from the VO) is given. The whole exercise is split into 7 learning portion.

Examples will be provided via TUWEL approx. one week before the particular exercise and should be self-studied beforehand. In the corresponding exercise you can compare your results to the ones presented in videos which will then be available in TUWEL. If any questions arise you can use the corresponding forum. After finishing a learning portion, there will be held a Zoom-Meeting where you can participate if you have any further questions.

There are more examples within the collection of examples than it is possible to present on the blackboard within the time frame of the exercise. These examples can be self-studied in order to prepare for the exams.

The exercises are based on the theory lectured on the corresponding VO! The exercises will only be fruitful, if you partcipate in parallel in the VO or you are familiar with basics of continuum mechanics (due to the application of the theoretical methods on practical problems).

Immanent

## Course dates

DayTimeDateLocationDescription
Wed12:00 - 14:0001.03.2023 - 28.06.2023GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Continuum Mechanics of Solids - Single appointments
DayDateTimeLocationDescription
Wed01.03.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed08.03.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed15.03.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed22.03.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed29.03.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed19.04.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed26.04.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed03.05.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed10.05.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed17.05.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed24.05.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed31.05.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed07.06.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed14.06.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed21.06.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine
Wed28.06.202312:00 - 14:00GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums LVA Termine

## Examination modalities

Two written exams, duration a 90min, collection of formulas can be used

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Wed12:00 - 14:0003.05.2023GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums assessed30.03.2023 10:00 - 01.05.2023 23:55TISS1. Kolloquium
Wed12:00 - 14:0014.06.2023GM 8/9 - Hörsaal des Internationalen Wiener Motorensymposiums assessed30.03.2023 10:00 - 12.06.2023 23:55TISS2. Kolloquium
Fri16:00 - 18:0030.06.2023FH Hörsaal 7 - GEO assessed03.05.2023 10:00 - 28.06.2023 23:55TISS1. Ersatzkolloquium
Fri16:00 - 18:0007.07.2023GM 4 Knoller Hörsaal - VT assessed03.05.2023 10:00 - 05.07.2023 23:55TISS2. Ersatzkolloquium

## Course registration

Begin End Deregistration end
02.03.2023 12:00 12.04.2023 12:00 10.05.2023 23:00

## Curricula

Study CodeSemesterPrecon.Info
033 245 Mechanical Engineering
Course requires the completion of the introductory and orientation phase
033 282 Mechanical Engineering - Management
Course requires the completion of the introductory and orientation phase
066 445 Mechanical Engineering
Course requires the completion of the introductory and orientation phase
066 482 Mechanical Engineering - Management
Course requires the completion of the introductory and orientation phase

## Literature

No lecture notes are available.

## Previous knowledge

Basics of matrix calculations

Basics of mechanics

German