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ME 6769: Linear Elasticity
Offered Every Fall
| Credit Hours: |
3-0-3 |
| Prerequisites: |
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. |
| Textbooks: |
Jacqueline R. Barber, Elasticity, Kluwer Academic Publishers, 1992. |
| Instructors: |
Iwona Jasiuk (ME), Chris Lynch (ME), Richard Neu (ME), Jianmin Qu (ME), Min Zhou (ME), Sathyanaraya Hanagud (AE) |
| 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. |
| Audience: |
First year graduate students in ME, AE, CE, and MSE. |
| Goals: |
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. |
| 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)
- Michells general solution (2h)
- Inclusion problems (3h)
- Contact problems (3h)
- Singular solutions (5h)
(Flamant solution, crack tip fields, dislocations)
- Greens 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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