AE1001 THEORY OF ELASTICITY 3 0 0 100
To understand the theoretical concepts of material behaviour with particular emphasis on their elastic property
1. ASSUMPTIONS IN ELASTICITY 4
Definitions- notations and sign conventions for stress and strain, Equations of equilibrium.
2. BASIC EQUATIONS OF ELASTICITY 15
Strain – displacement relations, Stress – strain relations, Lame’s constant –
cubical dilation, Compressibility of material, bulk modulus, Shear modulus, Compatibility equations for stresses and strains, Principal stresses and principal strains, Mohr’s circle, Saint Venant’s principle.
3. PLANE STRESS AND PLANE STRAIN PROBLEMS 8
Airy’s stress function, Bi-harmonic equations, Polynomial solutions, Simple two-dimensional problems in Cartesian coordinates like bending of cantilever and simply supported beams, etc.
4. POLAR COORDINATES 10
Equations of equilibrium, Strain displacement relations, Stress – strain relations, Axi – symmetric problems, Kirsch, Michell’s and Boussinesque problems.
5. TORSION 8
Navier’s theory, St. Venant’s theory, Prandtl’s theory on torsion, The semi- inverse method and applications to shafts of circular, elliptical, equilateral triangular and rectangular sections.
TOTAL : 45
1. Timoshenko, S., and Goodier, T.N., “Theory of Elasticity”, McGraw–Hill Ltd., Tokyo, 1990.
Enrico Volterra & J.H. Caines, “Advanced Strength of Materials”, Prentice Hall New Jersey, 1991.
Wng, C.T., “Applied Elasticity”, McGraw–Hill Co., New York, 1993.
Sokolnikoff, I.S., “Mathematical Theory of Elasticity”, McGraw–Hill New York, 1978.