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General


This course is part of the MAGIC core.

Description

This is offered as a core course for Applied. The objective is to derive in a rational way the governing equations for both solids and fluids and to solve a few illustrative problems. It is intended that, by the end of the course, students will have the knowledge necessary for the in-depth study of various phenomena in linear elasticity, nonlinear elasticity, rheology, and fluid mechanics.

Recommended books:
  • P. Chadwick, Continuum Mechanics, Dover (1999).
  • M.E. Gurtin, E. Fried and L. Anand, The Mechanics and Thermodynamics of Continua, CUP (2009).
  • O. Gonzalez and A.M. Stuart, A First Course in Continuum Mechanics, CUP (2008)
  • R.W. Ogden, Non-linear Elastic Deformations, Dover (1997).
  • P.G. Drazin and N. Riley, The Navier-Stokes equations: a classification of flows and exact solutions, Cambridge University Press (2006).
Semester

Autumn 2011 (Monday, October 10 to Friday, December 16)

Timetable
  • Mon 10:05 - 10:55
  • Wed 09:05 - 09:55

Lecturer


Yibin Fu
Email y.fu@maths.keele.ac.uk
Phone 01782 733650
Interests Solid mechanics
vcard
Photo of Yibin Fu


Students


Photo of Xiao Gai
Xiao Gai
(Loughborough)
Photo of Robert Hicks
Robert Hicks
(Cardiff)
Photo of Thorpe Maria
Thorpe Maria
(Manchester)
Photo of Pearce Philip
Pearce Philip
(Manchester)
Photo of Michael Walters
Michael Walters
(Cardiff)
Photo of Miao Yu
Miao Yu
(Loughborough)
Photo of Xizheng Zhang
Xizheng Zhang
(Loughborough)


Prerequisites


No prerequisites information is available yet.

Syllabus


  • Vector and tensor theory: Vector and tensor algebra, tensor product, eigenvalues and eigenvectors, symmetric, skew-symmetric and orthogonal tensors, polar decompositions, integral theorems.
  • Kinematics: The notion of a continuum, configurations and motions, referential and spatial descriptions, deformation and velocity gradients, stretch and rotation, stretching and spin, circulation and vorticity.
  • Balance laws, field equations: Mass, momentum, force and torque, theory of stress, equations of motion, energy.
  • Constitutive equations: Basic constitutive statement, examples of constitutive equations, observer transformations, reduced constitutive equations, material symmetry, internal constraints, incompressible Newtonian viscous fluids, isotropic elastic materials, viscoelastic materials, rheological models such as Reiner-Rivlin fluid and Bingham fluid.
  • Advanced formulations: Elementary continuum thermodynamics, variational formulations, conjugate measures of stress and strain, Hamiltonian formulations.
  • A selection of example problems: from Linear and Nonlinear Elasticity, and Fluid Mechanics.

Bibliography


Continuum Mechanics: Concise Theory and Problems Chadwick
A first course in continuum mechanics Gonzalez and Stuart
Non-Linear Elastic Deformations Ogden
The Navier-Stokes equations: a classification of flows and exact solutions Drazin, Riley and Society
Note:

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Assessment


No assessment information is available yet.

Assignments


Homework 1

Deadline: Friday 27 January 2012 (912.9 days ago)


Homework 2

Deadline: Friday 27 January 2012 (912.9 days ago)


Homework 3

Deadline: Friday 27 January 2012 (912.9 days ago)


Homework 4

Deadline: Friday 27 January 2012 (912.9 days ago)


Homework 5

Deadline: Friday 27 January 2012 (912.9 days ago)


Take-home exam

Deadline: Friday 27 January 2012 (912.9 days ago)


Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-5cm-chap1-3.pdfL
6-7cm-chap4.pdfL
7-9cm-chap5.pdfL
9-10cm-chap6-7.pdfL
10cm-complete-notes.pdf