Download MATH 364 - Continuum Mechanics

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Lahore University of Management Sciences
B.Sc. (Honours) Programme
MS Programme
Course Outline
Course: Continuum Mechanics (Math 364)
Pre-requisite: Linear Algebra (Math221), Multivariate Calculus (Math 103)
Quarter: Summer
Instructor: Dr. Wasiq Hussain
E-mail: [email protected]
Text: Nonlinear Solid Mechanics, A Continuum Approach for
Engineering, by Gerhard A. Holzapfel (2000). (John Wiley & Sons)
Reference book: Non-Linear Elastic Deformations by R.W. Ogden, 1997,
Dover Publications (New York).
Units: 4
Sessions: 5 lectures of 80 minutes per week
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At the microscopic level matter is discontinuous. It is composed of molecules and
atoms. However, in real life we are concerned with volumes of matter with
dimensions large compared with these particles. CONTINUUM MECHANICS
deals with the behaviour of bodies of solids and fluid matter on a macroscopic
scale. It disregards the microscopic structure and treats matter as being smoothly
distributed throughout the body under consideration.
GOALS:
1. To provide an introduction to the basic theoretical ideas in continuum mechanics
using the theory of CARTESIAN TENSORS.
2. Apply the theory in the solution of different types of problems in nonlinear
elasticity.
TEACHING PLAN:
WEEKS
TOPIC
READ
CHAPTER 1
Introduction to Vectors and Tensors
IST
(1) Algebra of vectors
Pages: 1 - 9
(2) Transformation laws for Basis Vectors
Pages: 28 - 32
and Components
IST
(3) Algebra of Tensors
Pages: 9 - 20
(4) Eigenvalues, Eigenvectors of Tensors
Pages: 24 – 27
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CHAPTER 2
KINEMATICS
2ND
(1) Configurations, and Motions of
Pages: 56 – 60
Continuum Bodies.
(2) Displacement, Velocity, Acceleration
Fields.
(3) Gradients and Related Operators (from
Chapter 1).
(4) Material, Spatial Derivatives.
(5) Deformation Gradient
2ND
(6) Strain Tensors
(7) Rotation, Stretch Tensors with applications
like SIMPLE SHEAR deformation.
(8) Rates of Deformation Tensors.
Pages: 61 – 64
Pages: 44 – 51
Pages: 64 – 69
Pages: 70 – 76
Pages: 76 – 84
Pages: 85 – 94
Pages: 95 - 105
CHAPTER 3
THE CONCEPT OF STRESS
3RD
(1) Traction Vectors, and Stress Tensors
Pages: 109 – 118
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CHAPTER 4
BALANCE PRINCIPLES
3RD
(2) Conservation of Mass
Pages: 131 – 138
(3) Integral Theorems (from Chapter 1)
Pages: 52 – 54
(4) Transport Formulae
3RD
Mid-Term
(5) Momentum Balance Principles
4TH
Pages: 138 – 140
(1) Balance of Mechanical Energy
Pages: 141 - 152
Pages: 152 - 160
CHAPTER 5
SOME ASPECTS OF OBJECTIVITY
4TH
(2) Objective Tensor Fields
Pages: 179 - 187
4TH
(3) Invariance of Elastic Material Response
Pages: 196 - 203
CHAPTER 6
HYPERELASTIC MATERIALS
4TH
(4) General Remarks on Constitutive Equations
Pages: 206 – 212
5TH
(1) Isotropic Hyperelastic Materials
Pages: 212 - 222
5TH
(2) Incompressible Hyperelastic Materials
Pages: 222 - 227
Grading:
40% Final.
30% Midterm.
30% Quizzes.
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