EML 5611

CONTINUUM MECHANICS

Fall 2004

Dr. N. Chandra

Dept of Mechanical Engineering

345 Engineering Building Phone: 410--6320

Class Hours: #9; #9;

Tuesday, Thursday 8:45 to 10:00 am

Office Hours:

Tuesday 2:00 to 4:00 pm

A. COURSE OBJECTIVE

To introduce the concept of the mechanics of deformation of

continuous media in general and that of solids in particular, and

To apply the principles to solve elastic boundary value

problems.

B. TEXTBOOK:

Introduction to continuous mechanics by W.M.~Lai,

D.~Rubin and E.~Krempl, Pergaman Press, Third Edition, 1993

C. REFERENCE BOOKS:

Theory of elasticity by S. Timoshenko and J.N.~Goodier,

Mc-Graw Hill Book Company, Second Edition, 1951.

Foundations of solid mechanics by Y.C. Fung, Prentice-Hall Inc, 1965.

Introduction to the mechanics of continuous medium

by L.E.~Malvern, Prentice-Hall Inc, Second Edition, 1979.

A first course in continuum mechanics by Y.C. Fung, Second

Edition, Prentice-Hall Inc., 1977

Tensor analysis, Theory and Application} by Sokolnikoff,

1951.

Vector analysis and Cartesian tensors with selected

applications by K. Karamcheti, Holden-Day Publishers, 1967.}

D. PREREQUISITES:

A graduate standing in mechanical engineering, or the approval of

instructor.

E. COURSE OUTLINE:

See the attached sheet.

F. GRADING SCHEME:

EML 5611

CONTINUUM MECHANICS

Course Outline

1. Introduction (2 Lectures)

Continuum Theory

Definition and Ramifications

Solids and Fluids

General Principles and Field Equations

 

2. Cartesian Tensor Theory (6 Lectures)

Indicial Notation

Scalars, Vectors, Tensors

Types and Order of Tensors

Tensorial Operations

Manipulation of Indicial quantities

Exam 1

3. Kinematics of Deformation (5 Lectures)

Displacement in Eulerian and Lagrangian descriptions

Engineering, Logarithmic, Almansi and Green strain

Pure and Simple Shear, Shear Strain

Plane strain and strain rosettes

Compatibility conditions

Velocity and Rate of Deformation

 

4. Stress (5 Lectures)

Definition

Stress vector and Tensor

Cauchys Formula

Equations of Equilibrium

Plane stress

Principal stress

Shearing stress

Boundary Conditions

Exam 2

5. Constitutive Equations of (4 Lectures)

Definition

Thermodynamic Constraints

Hooke's Law

Elasticity Tensor

Isotropy, Orthotropy, Anisotropy

Uniaxial and Multiaxial behavior

Experimental Determination of elastic constants

Newtonian Viscous Fluid

6. General Field Equations (6 Lectures)