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Theory of Elasticity

UNIT I:
Basic Equations of Elasticity:

Definition of Stress and Strain: Stress – Strain Relationships – Equations of Equilibrium,
Compatibility Equations, Boundary Conditions, Saint Venant’sprinciple – 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, Axis – Symmetric Problems, Introduction toDunder’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 forRectangular Plates
Under Different Boundary Conditions.

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