MEK4220 – Continuum Mechanics
Course description
Schedule, syllabus and examination date
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 (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. 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
Recommended previous knowledge
MAT1100 – Calculus, MAT1110 – Calculus and Linear Algebra, MAT1120 – Linear Algebra, FYS-MEK1110 – Mechanics and MEK1100 – Vector Calculus.
Overlapping courses
- 10 credits overlap with MEK2200 – Continuum Mechanics
- 10 credits overlap with MEK3220 – Continuum Mechanics (discontinued)
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
Three 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.
Explanations and appeals
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.