1. Review of Tensors. Calculus of Cartesian tensors. ( ~ 4 classes)
2. Orthogonal curvilinear coordinate systems - cylindrical, spherical, and polar coordinate systems. (~ 2 classes)
3. Introduction to elasticity. Relation between displacement and strain, strain transformation. Body and surface forces. Stress transformation. Principal stresses. Spherical, deviatoric, octahedral, and von Mises stresses. Equilibrium equation in differential form. Boundary conditions. Compatibility equations. (~ 3 classes)
4. Material behaviour. Hooke's law. Physical meaning of elastic constants. Different solution strategies. Strain energy and related principles. (~ 2 classes)
5. Two dimensional problem formulation. Plane stress. Plane strain. Airy stress function. Problems in rectangular and polar coordinates. (~ 10 classes)
6. Three dimensional problem formulation. Analysis of stress and strain. Some elementary problems. (~ 3 classes)
7. Torsion. Circular and non-circular cross section. Membrane analogy. Hydrodynamic analogy. (~ 2 classes)
8. Thermoelasticity. Heat conduction and the energy equation. Different formulations. (~ 3 classes)
9. Contact mechanics. Motion and forces at a point in contact. Line loading of an elastic half space. Point loading of an elastic half space. Normal contact of elastic solids - Hertz theory. Introduction to computational contact mechanics. (~ 10 classes)
Reference material
1. Timoshenko S. P., and Goodier J. N., Theory of Elasticity, McGraw-Hill Education (India), 3rd edition, 2010.
2. Sadd, M. H., Elasticity - Theory, Applications, and Numerics, Academic Press, 1st edition, 2005.
3. Barber J. R., Elasticity, Kluwer Academic Publication, 2002.
4. Johnson K. L., Contact Mechanics, Cambridge University Press, 1987.