18CV731 Theory of Elasticity syllabus for CV

Rigid and deformable bodies, body and surface forces, concept of stress, state of stress at a point, Cartesian stress components, Cauchey’s stress formula, stress transformation, principal stresses and principal planes, stress invariants, equations of equilibrium in 2D and 3D (Cartesian coordinates).

Types of strain, strain displacement relations, state of strain at a point, strain tensor, strain transformation, strain along a linear element, principal strains, strain invariants, octahedral strains, spherical and deviatoric strains.

Generalized Hooke’s Law, Stress-strain relationships, Equilibrium equations in terms of displacements and Compatibility equations in terms of stresses, Plane stress and plane strain problems, St. Venant’s principle, Principle of superposition, Uniqueness theorem, Airy’s stress function, Stress polynomials (Two Dimensional cases only). Equations of equilibrium in polar coordinate, compatibility equation, stress function.

Axisymmetric stress distribution - Rotating discs, Lame’s equation for thick cylinder, Effect of circular hole on stress distribution in plates subjected to tension, compression and shear, stress concentration factor.

Torsion:

Inverse and Semi-inverse methods, stress function, torsion of circular, elliptical, triangular sections.

Course outcomes:

After studying this course, students will be able to:

1. Ability to apply knowledge of mechanics and mathematics to model elastic bodies as continuum.

2. Ability to formulate boundary value problems; and calculate stresses and strains.

3. Ability to comprehend constitutive relations for elastic solids and compatibility constraints.

4. Ability to solve two-dimensional problems (plane stress and plane strain) using the concept of stress function.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.  There will be two full questions (with a maximum of four sub- questions) from each module.
• Each full question will have sub- question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Textbooks:

1. S P Timoshenko and J N Goodier, “Theory of Elasticity”, McGraw-Hill International Edition, 1970.

2. Sadhu Singh, “Theory of Elasticity”, Khanna Publishers, 2012.

3. S Valliappan, “Continuum Mechanics - Fundamentals”, Oxford &IBH Pub. Co. Ltd., 1981.

4. L S Srinath, “Advanced Mechanics of Solids”, Tata - McGraw-Hill Pub., New Delhi, 2003.

Reference Books:

1. C. T. Wang, “Applied Elasticity”, Mc-Graw Hill Book Company, New York,1953.

2. G. W. Housner and T. Vreeland, Jr., “The Analysis o f Stress and Deformation”, California Institute of Tech., CA, 2012.[Downloadasperuserpolicyfromhttp://resolver.caltech.edu/CaltechBOOK:1965.001].

3. A. C. Ugural and Saul K. Fenster, “Advanced Strength and Applied Elasticity”, PrenticeHall,2003.

4. Abdel-Rahman Ragab and Salah Eldinin Bayoumi, “Engineering Solid Mechanics: Fundamentals and Applications”, CRC Press,1998.