# MEK3220 – Continuum Mechanics

Choose semester

## Course content

Vectors and tensors. Index notation. Stress tensors for fluids and solids. Cauchy's relations. Principal stresses and principal directions. Velocities, displacement and acceleration. Deformation (strain). Relation between stress and strain. Newton's law of friction in fluids. Hooke's law for elastic matter. Simple viscous elastic models. The equation of motion for viscous fluids (the Navier Stokes equation). The equation of motion for isotropic linear elastic matter. Explicit solutions for equations for elastic matter: Stress distribution caused by gravity, axial strain, torsion of cylindrical rod, longitudinal and transversal waves (p- and s-waves), reflection of waves. Explicit solutions for equations for viscous fluids: Couette flow, laminar flow in pipes, flow on inclined planes, boundary layers. Equations of energy conservation, energy dissipation, equation of thermal transport, heat flow, Fourier's law. Thermally driven flow. Creep Flow. Scale analysis and principles and modeling.

## Learning outcome

To give an introduction to the basic equations and solution methods for mathematical modeling of viscous fluids and elastic matter. The course provides a basis for further studies in mechanics, applied and industrial mathematics, physics, geology, geophysics, and astrophysics.

## Admission

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

## Prerequisites

### Formal prerequisite knowledge

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

• Mathematics R1 (or Mathematics S1 and S2) + R2

And in addition one of these:

• Physics (1+2)
• Chemistry (1+2)
• Biology (1+2)
• Information technology (1+2)
• Geosciences (1+2)
• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).

## Overlapping courses

10 credits with MEK4200 – Viscous Flow and Elastic Media (discontinued).

10 credits with ME115, 7 credits with ME105, 5 credits with ME106, 5 credits with ME107 and 7 credits with ME116.

* The information about overlaps is not complete. Contact the department for more information if necessary.

## Teaching

Colloquia/exercises for the duration of one semester. The exercises are mainly based on independent work from the students. The students must hand in compulsory assignments.

## Examination

Two compulsory assignments have to be handed in and approved withing given deadlines to gain access to the final exam. Final mark is given based 100% on written examination at the end of the semester.

Rules for compulsory assignments at the Department of Mathematics.

### Examination support material

Rottmann's formula list + approved calculator.
Information about approved calculators (Norwegian only)

### Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

### Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

### Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

### Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

### Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

## Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

10

Bachelor

Every autumn

Every autumn

Norwegian

## Contact

Department of Mathematics