ME 1606 E2: ADVANCED MECHANICS OF SOLIDS 

Syllabus

Module I 
2D problems in Cartesian co-ordinates: 
stress & strain at a point, components of stress & strain , Hooks law plane stress & plane strain, measurement of surface strains, construction of Mohr circle for stress & strain , strain rosettes, differential equations of equilibrium , boundary conditions, compatibility equations, stress function. Solution by polynomials, St.Venant’s principle, bending of a cantilever loaded at the end. 

Module II 
2D problems in polar co-ordinates General equations in polar co-ordinates. Stress distribution symmetrical about an axis pure bending of curved bars. Strain components in polar coordinates, displacement for symmetrical stress distribution, rotating disks, thick cylinders, pure bending of curved bars. 

Module III 
Analysis of stress & strain in 3D 
Principal stresses, stress ellipsoid, stress invariants, maximum shearing stress, homogenous deformation. Strain at a point, rotation, differential equations of equilibrium, compatibility. Equations of equilibrium in terms of displacements Stretching of a prismatic bar by its own weight Energy methods: principle of virtual work, reciprocal theorems, strain energy methods, Castigliano’s theorems. 

Module IV 
Unsymmetric bending, shear flow, shear centre. 
Torsion of noncircular straight bars, elliptic cross sections. Membrane analogy. Torsion of thin tubes, open and closed sections. 

References : 
1) Theory of Elasticity : Timoshenko & Goedier, McGraw Hill 
2) Advanced Mechanics of Materials: Solecki & Conant: Oxford University Press 
3) Advanced Mechanics of Solids : L.S. Srinath, Tata McGraw Hill 
4) Solid Mechanics: SMA Kazimi, Tata McGraw Hill 
5) Advanced mechanics of materials : Boresi& Schmidt, Wiley 
6) Theory of Isotropic /Orthotropic elasticity – An introductory primer – K. Bhaskar & T.K Varadan, Ane Books 
Type of Questions for University Exam.
Q 1.Eight short answer questions of 5 marks with two questions from each of the four modules. (8x5 = 40 marks) 
Q 2. to Q.5 : Two questions A & B of 15 marks from each modules with option to answer either A or B. (4x15 = 60 marks)