MTech Mechanics Of Deformable Bodies syllabus for 1 Sem 2022 scheme 22CSE14

Theory of Elasticity:

Introduction: Definition of stress and strain and strain at a point, components of stress and strain at appoint of Cartesian and polar coordinates. Constitutive relations, equilibrium equations, compatibility equations and boundary conditions in 2-D and 3-D cases.

Transformation of stress and strain at a point,

Principal stresses and principal strains, invariants of stress and strain, hydrostatic and deviatric stress, spherical and deviatric strains max. shear strain.

Plane stress and plane strain:

Airy’s stress function approach to 2-D problems of elasticity, simple problems of bending of beams. Solution of axisymmetric problems, stress concentrationdue to the presence of a circular hole in plates.

Elementary problems of elasticity in three dimensions,

stretching of a prismatic bar by its own weight, twist of circular shafts, torsion of non-circular sections, membrane analogy, Propagation of waves in solid media. Applications of finite difference equations in elasticity.

Theory of Plasticity:

Stress – strain diagram in simple tension, perfectly elastic, Rigid – Perfectly plastic, Linear work – hardening, Elastic Perfectly plastic, Elastic Linear work hardening materials, Failure theories, yield conditions, stress – space representation of yield criteria through Westergard stress space, Tresca and Von- Mises criteria of yielding

Course outcomes:

On completion of this course, students are able to:

• Co1: Achieve Knowledge of design and development of problem solving skills.
• Co2: Understand the principles of stress-strain behaviour of continuum
• Co3: Design and develop analytical skills.
• Co4: Describe the continuum in 2 and 3- dimensions
• Co5: Understand the concepts of elasticity and plasticity

Question paper pattern:

• The question paper will have ten questions; each question carries equal marks,
• there will be two full questions or with a maximum of four sub questions from each module,
• students will have to attend five full questions from each module.

Reference Books:

1. Timoshenko &Goodier, “Theory of Elasticity”, McGraw Hill

2. Srinath L.S., Advanced Mechanics of Solids, 10th print, Tata McGraw Hill Publishingcompany, New Delhi, 1994.

3. Sadhu Singh, “Theory of Elasticity”, Khanna Publishers

4. Verma P.D.S, “Theory of Elasticity”, Vikas Publishing Pvt. Ltd

5. Chenn W.P and Hendry D.J, “Plasticity for Structural Engineers”, Springer Verlag

6. Valliappan C, “Continuum Mechanics Fundamentals”, Oxford IBH Publishing Co.Ltd.

7. Sadhu Singh, “Applied Stress Analysis”, Khanna Publishers

8. Xi Lu, “Theory of Elasticity”, John Wiley.