Teaching Material
Slides
Exercises
Previous Exams
Plan from previous years
- Sep 8: Read through all introductory examples
on the slides until the "Lagrangian
description" part. The "Circular Couette" flow example with
advanced use of cylindrical coordinates can be skipped in this round.
Exercises: 1.3, 2.5, 2.6. 3.2 (Martin's group); 1.1, 1.2, 2.1, 2.2, 3.1
(Fredrik's group).
- Sep 15: Joakim Sundnes presents the slides from "Lagrangian description"
and continues with "Fundamental laws".
Exercises: 5.1 and 5.2 (about symmetry of scalar and vector fields).
- Oct 6: Exercises 1.5, 1.7, 1.8, 1.9, 3.3, 3.4, 2.7, 2.8.
- Oct 20: slides 381-491, exercises 1.7, 1.10, 2.12, 2.13, 2.14,
- Oct 27: Exercises 2.15, 2.16, 2.17, 2.18, 3.5, 3.6, 3.7, 3.8.
Slides to read: 382-500.
- Nov 3: Same exercises as last week. Slides including plasticity.
- Nov 10: Exercises 2.19, 2.20, 3.7, 3.8, 4.1, 4.2
- Nov 17: We go through previous exams,
this time 1999 and 2000.
- Nov 24: More previous exams,
this time 1996 and 1998. Joakim is the teacher.
This is the last time we meet before the exam,
unless you have specific requests.
Exam (from 2004)
A couple of exercises from this collection:
previous exams 1996, 1998, 1999, 2000, and regular exercises
1.1, 1.2, 1.3, 1.5, 1.7, 1.8, 1.9, 1.10, 2.5, 2.6, 2.7, 2.8, 2.12, 2.13, 2.14,
2.15, 2.16, 2.17, 2.18, 2.19, 2.20, 3.1, 3.2, 3.3, 3.4,
3.5, 3.6, 3.7, 3.8, 4.1, 4.2.
Exam (from 2003)
You will get some of the exercises listed below at the exam. The
exercises might be slightly altered: notation may shift and questions may
be removed or made shorter. If you have understood the original exercise,
there should be no surprises at all.
In addition to previous relevant exams and the set of exercises you can get the following toretical questions:
- Derive the Navier-Stokes equations for incompressible fluid flow.
- Derive the equations of gas dynamics.
- Derive Navier's equation of elasticity for heterogeneous materials,
with thermal effects (thermal strain) incorporated.
- Mention four different physical applications of the Laplace equation and present a
derivation of the equation in each case (it is sufficient to start with a
general PDE for some phenomenon and explain how it is simplified to the
Laplace equation).
- Define plane stress and plane strain. Set up the associated PDE models.
- What is Airy's stress function? When can you apply it?
- What is the difference between a Bingham fluid and a power-law fluid?
- Explain a type of applications
where you need to apply the compatibility equations.
Note 2:
- There are far too many questions about scaling these days.
Scaling is a topic, but it is difficult and does not deserve the
attention it has received among the students in this course.
When you go through the exercises, make sure you can perform the
technical steps of scaling, but don't dive into lengthy discussions
about different choices of time scales before you are very well prepared
for all other types of questions.
On the exam non-trivial scales will be given.
Note 2:
- On the exam you can bring with you one sheet of paper. You can
write whatever you want on this sheet, but you have to hand it in together
with your answers to the exercises. In case we need to judge whether you
should get an A or a B this sheet of paper (normally with an overview
of important things) will be looked at.
Book
A recommended (classical) textbook is George Mase: Continuum
Mechanics,
Schaum's Outline Series, McGraw-Hill, 1970. It is quite cheap and for sale
in the Akademika bookstore at campus.
Alternatives exists, e.g., Hunter: Mechanics of Continuous Media, and
Malvern: Introduction to the Mechanics of Continuous Media
(comprehensive).
None of these are in the bookstore.
Students in the past have reported that they use Mase now and then in
the beginning of the course, but that the intensive work with the
course consists in reading slides and studying the exercises.
Lectures
- September 2 and 3:
Characteristics of the course, notation, introduction to forces and stress.
- September 9:
More about stress (normal and shear stress), the general basic models
for heat conduction, elasticity, and viscous flow.
- September 10:
Meeting with all students who plan to take an exam in this course.
Decision regarding the amount and type of exercises we need and how to
organize the problem solving sessions.
- September 16:
Examples on adapting
general models for elasticity, heat transfer, and fluid flow to
specific problems. Scaling.
- September 17:
Meeting about this week's exercises.
- September 23:
Strain, deformation, large deformations, infinitesimal deformation
approximation, Lagrange and Euler formulations.
Joakim Sundnes teaches.
- September 24:
Canceled.
- September 30:
Topic to be announced by Joakim on Sept. 23.
- October 1:
Canceled.
- October 7:
Hans Petter is back with more examples on adapting general models
to specific problems. Probably some more about scaling.
- October 8:
Special exercise (see link above) about two-fluid flow in a channel.
- October 14:
Probably 3 hours with exercises.
- October 8:
More exercises.
- October 21:
Fundamental laws of continuum mechanics; a framework based on
mass balance, Newton's 2nd law of motion, and the 1st law of
thermodynamics.
- October 22:
More exercises.