MAGIC090: Introduction to Continuum Mechanics

Course details

A core MAGIC course

Semester

Autumn 2018
Monday, October 8th to Friday, December 14th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Thursdays
11:05 - 11:55

Description

The theory of continuous media is the common denominator of several physical theories concerned with the global (macroscopic) behaviour of substances under the influence of external agents. Two main examples of such theories are fluid mechanics and elasticity theory. The main feature which distinguishes continuum mechanics from other physical theories like, for example, quantum mechanics, is that all the fine microscopic details are disregarded; in particular, it is assumed that the highly discontinuous structure of matter can be replaced by a smoothed hypothetical body. Quantities such as density, displacement and velocity (the so-called field variables) are taken to be continuous functions of position and their values are calculated via axiomatic rules.
In this course we develop the general mathematical apparatus required for the analysis of the deformation of solids and the flow of fluids. An understanding of continuum mechanics is of paramount importance in many applications, including meteorology, seismology, chemical engineering, biomechanics, civil engineering, aircraft design, etc.

Prerequisites

Vector Calculus, Linear Algebra, Newtonian Dynamics

Syllabus

1. Vectors and tensors.
2. Kinematics (the geometry of deformation and strain).
3. Balance Laws (mechanical stress, Cauchy's equation of motion)
4. Constitutive behaviour (objectivity, elastic materials, hyperelasticity, incompressibility)
5. Linear elasticity and boundary-value problems.

Lecturer

  • CC

    Ciprian Coman

    University
    University of Nottingham

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

  • Course on Continuum Mechanics (Ciprian D. Coman, )
  • Continuum Mechanics (Peter Chadwick, book)
  • An Introduction to Continuum Mechanics (Morton E. Gurtin, book)
  • The Linearized Theory of Elasticity (William S. Slaughter, book)
  • Non-Linear Elastic Deformations (Raymond W. Ogden, book)
  • Introduction to the Mechanics of a Continuous Medium (Lawrence E. Malvern, )

Assessment

Description

The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. There will be 5 questions and you will need the equivalent of 3 questions to pass.

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Files

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Lectures

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