ME 6769 Linear Elasticity

ME 6769: Linear Elasticity
Offered Every Fall

Hours:	3-0-3
Prerequisite:	Knowledge of strength of materials and differential equations is required to take the class. Knowledge of continuum mechanics is strongly recommended.
Catalog Description:	Governing equations of linear elasticity, plane elasticity, boundary value problems, Airy stress function and complex variable methods, simple three dimensional solutions. Crosslisted with AE 6769.
Textbook:	Jacqueline R. Barber, Elasticity, Kluwer Academic Publishers, 1992.
Instructors:	Iwona Jasiuk (ME), Chris Lynch (ME), Richard Neu (ME - Fall 2003), Jianmin Qu (ME), Min Zhou (ME), Sathyanaraya Hanagud (AE - Fall 2004)

References:

A.P. Boresi and K.P. Chong, Elasticity in Engineering Mechanics, Elsevier, 1987.
A.E. Green and W. Zerna, Theoretical Elasticity, 1968.
R.W. Little, Elasticity,1973.
A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 1944.
N. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, 1953.
I.S. Sokolnikoff, Mathematical Theory of Elasticity.

Goal:

This class will introduce governing equations of linear elasticity and will focus on solutions of boundary value problems in both two and three dimensions using several different methods.

Audience: First year graduate students in ME, AE, CE, and MSE.

Topics:

Governing Equations of Linear Elasticity

(Review of Continuum Mechanics Concepts)

- Traction, stresses, equilibrium equations (2h)

- Deformation, strains, compatibility conditions (2h)

- Constitutive equations (1h)

- Boundary conditions (1h)

Uniqueness of Solution

St. Venant Law

Plane Elasticity

- Plane stress and plane strain (1h)

- Airy stress function method (20h)

- Problems in Cartesian coordinates (4h)

- Problems in polar coordinates (14h)

* Curved beams (1h)

* Michell’s general solution (2h)

* Inclusion problems (3h)

* Contact problems (3h)

* Singular solutions (5h)

(Flamant solution, crack tip fields, dislocations)

- Green’s function method (2h)

- Complex variables method (3h)

- Dundurs constants (1h)

Three-dimensional Elasticity

- Displacement potentials method (2h)

- Radial symmetric problems (4h)

- Torsion of prismatic bars (4h)

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Revised June 2004