Unit 1

Analysis of Stress and Strain: Stress at a point; stress tensor; stress transformations; principal stresses; octahedral stress; geometrical representation of stress at a point; equations of equilibrium.

Infinitesimal affine transformation for deformation; strain tensor; principal strains; strain-displacement relations for finite and infinitesimal strains; compatibility conditions. Constitutive Equations: General theory; generalized Hooke’s law for anisotropic and isotropic materials.

Unit 2

Equations of Elasticity: Common equations of elasticity theory like Mitchel-Beltrami and Navier equations, formulation of the general elasticity problem; boundary conditions

Unit 3

Solution of Some Special Boundary Value Problems: Simplifications; two-dimensional problems in rectangular and polar coordinates; Airy’s stress function; a few problems like stress concentration around a circular hole and Boussinesq problem.

A few representative three-dimensional problems; torsion and bending of non – circular prismatic bars (Saint- Venant’s solution); membrane analogy, Simple Plate bending

Course Objectives

• Expose students to the theoretical fundamentals of elasticity
• Inculcate knowledge on basic governing equations of elasticity

Course Outcomes

• CO1: Apply principles of elasticity theory to estimate stresses and strains in isotropic and non isotropic materials using a tensorial approach.
• CO2: Formulate and solve boundary value problems in solid continua using stress and displacement based solution Strategies.
• CO3: Formulate and solve planar problems using Airy stress function in rectangular and polar co-ordinates
• CO4: Solve specific three-dimensional problems like torsion, bending of non-circular prismatic bar, membrane analogy and simple plate bending

CO – PO Mapping

Textbook(s)

• Timoshenko S. P. and Goodier J. N. – ‘Theory of Elasticity’- McGraw Hill International Editions, 1970 – 3^rd Edition
• L. S. Srinath – ‘Advance Mechanics of Solids’ – McGraw Hill Education – 2009 – 3^rd Edition

Reference(s)

• Hartog, J. P. D. – ‘Advanced Strength of Materials’- Dover Publications Inc, – 1987
• Boresi A. P., Schmidt R. J. and Sidebottom O. M. – ‘Advanced Mechanics of Materials’ -John Wiley & Sons Inc. – 1993 – 6^th Edition
• Durelli A. J., Phillips E. A. and Tsao C. H. – ‘Introduction to the Theoretical and Experimental Analysis of Stress and Strain’ – McGraw Hill, New York – 1958.

Evaluation Pattern