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.
  • 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)