Lecture Notes
Syllabus
Strain: Tensor notations - Displacement field – engineering strain – strain tensor – Strain-displacement relations – Compatibility conditions – Strain transformation – Principal strains and planes. Stress: Stress at a point – Traction vector and Stress tensor – Stress components in rectangular coordinate systems – Cauchy’s equations. Stress transformation – Principal stresses and planes – Hydrostatic and deviatoric stress components – Octahedral stress – Equations of equilibrium.
Constitutive Relations: Generalized Hooke's law – Stress-Strain relations for isotropic materials – Elastic constants – Relation between elastic constants - anisotropy. Saint-Venant's principle for end effects – General theorems of uniqueness, Linear superposition, and reciprocity – Castigliano’s Theorem, thermoelastic behavior of materials.
2D Elasticity: Plane stress and plane strain problems – Stress compatibility equation – Airy’s stress function and equation – Polynomial method of solution – Solution for bending of a cantilever beam with an end load
Elastic Problems in Polar Coordinates: Analogy between polar and rectangular coordinates – Equilibrium equations – Airy’s stress function in polar coordinates – Application in Stress Concentration problems – Axisymmetric problems – plate with a hole - Thick-walled cylinder and rotating discs.
Unsymmetrical Bending: Unsymmetrical bending of straight beams – Curved beams – Shear center of thin-walled open sections with one axis of symmetry. Torsion: Torsion of non-circular bars – Solutions for circular and elliptical cross-sections using Saint-Venant's theory and Prandtl’s method – Torsion of thin-walled tubes – Shear flow.
References
1. Timoshenko, S. and Goodier, J.N., 2010. Theory of Elasticity. Tata McGraw-Hill.
2. Arthur P Boersi, Richard J Schmidt, 2002. Advanced Mechanics of Materials, Wiley Publications, ISBN: 978-0-471-43881-6.
3. Sadd, M.H., 2009. Elasticity: Theory, Applications, and Numerics. Elsevier Academic Press.
4. Srinath, L.S., 2008. Advanced Mechanics of Solids. Tata McGraw-Hill.
5. Dym, C.L. and Shames, I.H., 2013. Solid Mechanics: A Variational Approach. Springer.
6. Popov, E.P., 2015. Engineering Mechanics of Solids. Pearson Education India.