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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 indepth 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, Nonlinear Elastic Deformations, Dover (1997).
 P.G. Drazin and N. Riley, The NavierStokes 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
Prerequisites
No prerequisites information is available yet.
Syllabus
 Vector and tensor theory: Vector and tensor algebra, tensor product, eigenvalues and eigenvectors, symmetric, skewsymmetric 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 ReinerRivlin 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
Note:
Clicking on the link for a book will take you to the relevant Google
Book Search page. You may be able to preview the book there. On the
right hand side you will 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.)
Assessment
No assessment information is available yet.
Assignments
Homework 1
    Deadline:  Friday 27 January 2012 (977.4 days ago) 
Homework 2
    Deadline:  Friday 27 January 2012 (977.4 days ago) 
Homework 3
    Deadline:  Friday 27 January 2012 (977.4 days ago) 
Homework 4
    Deadline:  Friday 27 January 2012 (977.4 days ago) 
Homework 5
    Deadline:  Friday 27 January 2012 (977.4 days ago) 
Takehome exam
    Deadline:  Friday 27 January 2012 (977.4 days ago) 
Files
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