Syllabus
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Course Code: Elective 1 MMATH21 -307 Course Name: Elasticity |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Extension : Extension of beams by longitudinal forces, Beam stretched by its own weight,
Bending of beams by terminal couples. Torsion : Torsion of a circular shaft, Torsion of cylindrical bars, Torsional rigidity. Torsion and stress functions. Lines of shearing stress. Torsion of elliptic cylinder. Simple torsion problems, effect of grooves. |
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| 2 | Torsion of rectangular beam, Torsion of triangular prism. Solution of torsion problems by means of conformal mapping. Torsion-membrane analogy, Torsion of hollow beams, Torsion of anisotropic beams. Flexure of beams by terminal loads, Flexure of circular and elliptic beams, Bending of rectangular beams, Bending of circular pipes. | |
| 3 | Two dimensional problems : Plane deformation, Generalized plane stress, Plane elastostatic problems, . Airy stress function. General solution of biharmonic equation, Stresses and displacements in terms of complex potentials. The structure of functions φ(z) and ψ(z). First and second boundary value problems in plane elasticity. Existence and uniqueness of the solutions. | |
| 4 | Three dimensional problems: General solutions; Concentrated forces; Deformation of elastic half-space by normal loads; The problem of Boussinesq. Elastic sphere: pressures, harmonics, equilibrium. Betti’s Integration method. Vibrations of elastic solids, Wave propagation in infinite regions, Surface waves. | |
