## Course Detail

 Course Name Theory of Elasticity Course Code 19MEE339 Program B. Tech. in Mechanical Engineering Year Taught 2019

### Syllabus

##### 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

### Objectives and Outcomes

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

 PO/PSO/ CO PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3 CO1 3 3 3 2 1 3 2 1 CO2 3 3 3 3 2 3 2 1 CO3 3 3 3 3 2 3 2 1 CO4 3 3 2 2 2 3

### Textbook / Reference

Textbook(s)

• Timoshenko S. P. and Goodier J. N. – ‘Theory of Elasticity’- McGraw Hill International Editions, 1970 – 3rd Edition
• L. S. Srinath – ‘Advance Mechanics of Solids’ – McGraw Hill Education – 2009 – 3rd 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 – 6th 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

 Assessment Internal External Periodical 1 15 – Periodical 2 15 – *Continuous Assessment (CA) 20 – End Semester – 50 *CA – Can be Quizzes, Assignment, Projects, and Reports.

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