CAE356 Theory of Elasticity Syllabus:
CAE356 Theory of Elasticity Syllabus – Anna University Regulation 2021
OBJECTIVES:
• To study the effect of periodic and a periodic forces on mechanical systems
• To learn the natural characteristics of large sized problems using approximate methods.
• To learn the concepts of plane stress and plane strain problems
• To understand the natural frequency of vibrations of the beams and torsional vibrations of systems.
• To make students aware of theory of plates and shells
UNIT I BASIC EQUATIONS OF ELASTICITY
Definition of Stress and Strain: Stress – Strain relationships – Equations of Equilibrium, Compatibility equations, Boundary Conditions, Saint Venant’s principle – Principal Stresses, Stress Ellipsoid – Stress invariants.
UNIT II PLANE STRESS AND PLANE STRAIN PROBLEMS
Airy’s stress function, Bi-harmonic equations, Polynomial solutions, Simple two-dimensional problems in Cartesian coordinates like bending of cantilever and simply supported beams.
UNIT III POLAR COORDINATES
Equations of equilibrium, Strain – displacement relations, Stress – strain relations, Airy’s stress function, Axi – symmetric problems, Introduction to Dunder’s table, Curved beam analysis, Lame’s, Kirsch, Michell’s and Boussinesque problems – Rotating discs.
UNIT IV TORSION
Navier’s theory, St. Venant’s theory, Prandtl’s theory on torsion, semi- inverse method and applications to shafts of circular, elliptical, equilateral triangular and rectangular sections. Membrane Analogy.
UNIT V INTRODUCTION TO THEORY OF PLATES AND SHELLS
Classical plate theory – Assumptions – Governing equations – Boundary conditions – Navier’s method of solution for simply supported rectangular plates – Levy’s method of solution for rectangular plates under different boundary conditions.
TOTAL: 45 PERIODS
COURSE OUTCOMES:
At the end of the course, Students will be able to
CO1: Estimate the linear elasticity in the analysis of structures such as beams, plates etc.
CO2: Determine the facture mechanics of the curved beam subject to loads.
CO3: Interpret the two dimensional problems in cartesian and polar coordinates
CO4: Determine the response of elastomers based objects
CO5: Explain the structural section subjected to torsion
TEXT BOOKS:
1. Ansel C Ugural and Saul K Fenster, ‘Advanced Strength and Applied Elasticity’, 4th Edition, Prentice Hall, New Jersey,4th edition 2003.
2. Bhaskar, K., and Varadan, T. K., Theory of Isotropic/Orthotropic Elasticity, CRC Press USA, 2009.
3. Timoshenko, S.P, and Goodier, T.N., Theory of Elasticity, McGraw – Hill Ltd., Tokyo, 1990.
REFERENCES:
1. Barber, J. R., Elasticity (Solid Mechanics and Its Applications), Springer publishers, 3rd edition, 2010.
2. Sokolnikoff, I. S., Mathematical Theory of Elasticity, McGraw – Hill, New York, 1978.
3. Volterra& J.H. Caines, Advanced Strength of Materials, Prentice Hall, New Jersey, 1991.
4. Wang, C. T., Applied Elasticity, McGraw – Hill Co., New York, 1993.