ME 821 Linear Elasticity

 Prerequisite: ME 820 - Continuum Mechanics.

Instructor: T. J. Pence, 2452 EB, 353-3889, pence@egr.msu.edu.

Time and Place: TTh 8:00-9:20  in 1202 EB

Required Text: The Linearized Theory of Elasticity, W.S. Slaughter, Birkhauser, 2002

Course Rationale: This course is intended to be a rigorous, mathematically based, introduction to linear elasticity.  It is intended for students who seek a fundamentally strong grounding in linear elasticity in order to do research, and to take further graduate courses in those areas of solid mechanics that presume a good understanding of linear elasticity (e.g. ME 824, ME 921, ME 922).  Students who seek a graduate class that provides a more applied approach to engineering stress analysis of solids are encouraged to consider the alternative class ME 828 - Advanced Strength of Materials, which, while still math-based, does not lean so heavily on tensor analysis and partial differential equations. 

Course Description: Fundamentals of isotropic linear elasticity. Solution of plane elasticity problems. St. Venant bending and torsion. Singular solutions. Basic three-dimensional solutions.  Here is a provisional schedule of topics is as follows: 

1. Review of material assummed to be known: indicial notation, stress concepts, strain definition, strain compatability.

2.  Stress-strain relation for linear elasticity in terms of elastic constants, reduction to two independent elastic constants for isotropic materials.

3. Complete sets of field equations, basic boundary value problems, superposition.

4.  Reciprocol theorem, energy identity, uniqueness theorem.

5.  Two dimensional problems, plane strain, plane stress, Airy stress function.

6.  St. Venant problems for extension, bending, torsion, and flexure.

7.  Basic potential function in three-dimensional elastostatics, the biharmonic equation.

8.  Singular solutions, the Kelvin state, doublets.

9.  Pressurized spheres and cavities.

10.  Problems for a half-space, half-line of dilitation,  punch problems.

11.  Introduction to elastodynamics.

Grading: Grades will be assigned on the basis of homework (34%), a  midterm exam (33% each) and a final exam (33%). You may expect from five to seven homework assignments. The final exam is scheduled for 7:45 am, Thursday May 3.

Policy: The due dates for the homework will be announced in class for the individual assignments. A limited degree of mutual assistance on homework is permissible, but all submitted assignments must utlimately be the student's own work. No late homework will be accepted for grading. Students are expected to attend lectures and class absence is no excuse for being unaware of announcements or course materials. The instuctor is not responsible for providieng lecture notes due to a student's absence. Students are on their honor to neither seek nor give unauthorized support or assistance on the Midterm and Final, nor to seek any unfair advantage over other students. Students are responsible for the security of their examination papers.