AO4002 Theory of Elasticity Syllabus:
AO4002 Theory of Elasticity Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
This course will enable students
1. To learn the basic concepts and equations of elasticity.
2. To provide with the concepts of plain stress and strain related problems.
3. To gain knowledge on equilibrium and stress-strain equations of polar coordinates.
4. Will be exposed to axisymmetric problems.
5. To get insight into the basic concepts of plates and shells.
UNIT I BASIC EQUATIONS OF ELASTICITY
Definition & sign convention for stress and strain – Hooke’s law – Relation between elastic constants – Equilibrium and compatibility equations – Analysis of stress, strain and deformation – Stress and strain transformations equations – Cauchy’s formula – Principal stress and principal strains in 2D & 3D – Octahedral stresses and its significance – Boundary conditions.
UNIT II APPLIED CONCEPTS
Plane stress and plane strain problems – Airy stress function – Biharmonic equation – Compatibility equation in terms of stress – Solution of bar and beam problems using the elasticity approach – Torsion of bars – Determination of stresses, strain and displacements – Warping of cross-sections – Prandtl’s stress function approach – St. Venant’s method.
UNIT III POLAR COORDINATES
Strain-displacement relations in polar coordinates – Equilibrium and stress-strain equations in polar coordinates – Infinite plate with a small central hole – Stress concentration – Bending of a curved beam (Winkler-Bach theory) – Deflection of a thick curved bar – Stresses in straight and curved beams due to thermal loading – Thermal stresses in cylinders and spheres – Stress concentration in bending.
UNIT IV AXISYMMETRIC PROBLEMS
Equilibrium and stress-strain equations in cylindrical coordinates – Lame’s problem – Thick walled cylinders subject to internal and external pressure – Application of failure theories – Stresses in composite tubes – Shrink fitting – Stresses due to gravitation – Analysis of a rotating disc of uniform thickness – Discs of variable thickness – Rotating shafts and cylinders.
UNIT V PLATES AND SHELLS
Classical plate theory – Assumptions, governing equations and boundary conditions – Navier’s method of solution – Levy’s method of solution – Rectangular and circular plates – Solution techniques – Analysis of a shell – Membrane Theory – Deformation and stresses due to applied loads.
TOTAL: 45 PERIODS
COURSE OUTCOMES:
Upon completion of this course, students will
CO1:Have knowledge of basic elasticity relationships and equations.
CO2:Know how to carry out stress analysis in 2-D and 3-D.
CO3:Get exposure on the formulation of constitutive and governing equations for basic problems in cartesian and cylindrical coordinates.
CO4:Be able to analyse and solve practical problems in cartesian and cylindrical coordinates.
CO5:Be able to determine the stress, strain and displacement field for common axisymmetrical members.
REFERENCES:
1. Harry Kraus, “Thin Elastic Shells”, John Wiley and Sons, 1987.
2. Flugge, W, “Stresses in Shells”, Springer – Verlag, 1990.
3. Timoshenko, S.P. and Gere, J.M, “Theory of Elastic Stability”, McGraw Hill Book Co. 2010.
4. Timoshenko, S.P. Winowsky. S., and Kreger, “Theory of Plates and Shells”, McGraw Hill Book Co., 2nd edition, 2015.
5. Varadan, TK andBhaskar,K, “Analysis of plates-Theory and problems”, Narosha Publishing Co., 2001.