When a body is subjected to external loads, internal stress is induced in the body and the body deforms accordingly. If the body restores its original shape as the external loads are removed, it is called an elastic body. On the other hand, if the loading is so large such that permanent deformation takes place, the response of the body is inelastic. Usually engineering materials are designed to behave in the elastic range. The objective of the course is to discuss methods that can be used to analyze the stress and deformation of elasitic bodies under external loading.

The students should acquire the following knowledge as the semester ends:

1. various measures to describe the deformation of a body, the physical meanings and the transformation of these measures, and compatibility condtions of strains.
2. relation between stress vector and stress tensor; equations of motion, principal stress, and maximum shearing stress.
3. hyperelastic materials and the generalized Hooke’s law, isotropic materials, and the relation between elastic constants and engineering constants.
4. formulation of elasticity problems in rectangular, cylindrical, and spherical coordinate systems, and the principle of virtual work.
5. analysis of problems with only on independent variables, such as a spherical shell subjected to internal pressure.
6. analysis of plane strain and plane stress problems, and the airy stress function.
7. analysis of torsion problems.
8. analysis of bending problems and the Timoshenko beam theory.