Prerequisites: MATH 2263 or equiv., AEM 4501 or equiv., or Instructor Approval.

Introduction to the theory of elasticity, with emphasis on linear elasticity. Linear and nonlinear strain measures, the boundary value problem for linear elasticity, plane problems in linear elasticity, and three dimensional problems in linear elasticity. Other topics will be selected from nonlinear elasticity, micromechanics, contact problems and fracture mechanics.

Textbook: Required: Elasticity: Tensor, Dyadic, and Engineering Approaches, Chou/Pagano, Dover, ISBN: 0486669580; Optional: Elasticity: Theory, Applications, and Numerics 2nd Edition, Sadd, Academic Press, ISBN: 0123744466

Summary

This course is aimed at first year graduate students and advanced undergraduates interested in the theory and method of solution for problems involving linear elastic materials.

Linear elasticity is perhaps one of the most successful theories in mechanics. It is used to design almost all structures, vehicles and machines that are in use today. Linear elasticity has also been found to be able to describe atomic motions of dislocations in ductile metals. This course introduces the basic equations of linear elasticity and types of problems. The uniqueness theorem is proved which gives insight into what makes a problem properly posed in this theory. The classical solutions of St. Venant for extension, bending, torsion and flexure are presented and compared with the strength of materials solutions. Two dimensional plane problems, both plane-strain and plane-stress are developed and then methods of solution, such as the Airy stress function, are covered including the Mode I and II singular crack solutions. Energy methods, which are often the basis for Finite Element Methods, are introduced along with the calculus of variations. As an example a plate theory is developed.

The grade in this course is based on homework assignments, a midterm and final exam.