Objectives

The objective of the course is to equip students with the capability of solving boundary value problems in small deformation linear elasticity and thermoelasticity using various mathematical methods involving direct solution and energy minimization techniques. This course has ESO202 (Mechanics of Solids) as a prerequisite.

Course content

Vector and tensor calculus; Concept of strain; Concept of stress; Equilibrium; stress-strain relationship; Boundary value problem of linear elasticity; Plane stress and plane strain problems; Axisymmetric problems; Torsion of non-circular sections; Contact problems; Wedge problems; Exposure of 3-d problems in elasticity; Energy methods; Special topics.

Total number of lectures: 40

Lecturewise breakup

1. Tensor algebra and calculus: 3 Lectures

2. Strains: 3 Lectures

• Concept of strain, derivation of small strain tensor and compatibility

3. Stress: 3 Lectures

• Concept of stress, Cauchy stress, equilibrium and equations, principal stresses and directions

4. Constitutive equations: 2 Lectures

• Generalized Hooke’s law including thermoelasticity, material symmetry

5. Formulation of the bvp in linear elasticity including: 2 Lectures

• Concepts of uniqueness and superposition, 2-d plane stress and plane strain problems.

6. Introduction to governing equations in cylindrical and spherical coordinates, axisymmetric problems: 2 Lectures

7. Curved beams: 3 Lectures

8. Torsion of non-circular cross sections: 3 Lectures

9. Contact problems in 2-d: 4 Lectures

10. Problems on wedges and crack tip fields: 3 Lectures

11. 3-d problems by potential/Fourier-transformation methods: 4 Lectures

12. Energy methods: 4 Lectures

13. Special topics (to be decided by the instructor, e.g., fracture, contact mechanics, wave propagation in solids, etc.): 4 Lectures

Recommended books

1. Barber, Elasticity, Springer (3rd Edition), 2010

2. Slaughter, The Linearized Theory of Elasticity, Birkhäuser, 2002

3. Bower, Applied Mechanics of Solids, CRC Press, 2009

4. Saad, Elasticity: Theory, Application and Numeric, Academic Press, 2004

5. Landau and Lifshitz, Theory of Elasticity (3rd Edition), Butterworth-Heinemann, 1984

6. Lurie, Theory of Elasticity, Springer, 2005

Proposing instructors: Dr. S. Basu, Dr. A. Gupta, Dr. U. Roy