IIT Guwahati Solid Mechanics-II Syllabus
ME 223. Solid Mechanics – II (3-0-0-6)
Pre-requisite: ME 212 or equivalent.
Analysis of stresses: 3D state of stress at a point; principal stresses; invariants; 3D Mohr’s circle; octahedral stresses; hydrostatic and pure shear stresses. Differential equations of equilibrium in rectangular and polar coordinates. Boundary conditions. Saint-Venant’s principle, Principle of superposition. Analysis of strains: 3D strain components in rectangular and polar coordinates; state of strain at a point; principal strains; strain deviators and invariants. Compatibility conditions in rectangular and polar coordinates. Constitutive relations. Boundary value problems: Stress formulation and displacement formulation; Beltrami-Michell equations and Navier’s equations. Methods of solution and uniqueness of solution. Plane problems: Plane stress and plane strain problems. Airy stress function. 2D problems in rectangular and polar coordinates and axisymmetric problems: Cantilever beam with end load; uniformly loaded beam; thick and thin walled cylinders; rotating discs and cylinders; plate with a circular hole. Curved beams. Torsion of non-circular bars: Saint-Venant’s semi-inverse method; Prandtl’s stress function method. Unsymmetrical bending, shear center and shear flow. Energy methods: Principle of virtual work; minimum potential energy; statically indeterminate systems. Elastic stability: Analysis of beam columns. Yield and Fracture criteria: Different failure theories; stress space and strain space; yield surfaces. Introduction to plasticity.
 S. P. Timoshenko and J. N. Goodier, Theory Of Elasticity, McGraw Hill International, 2010
 L. S. Srinath, Advanced Mechanics Of Solids, Tata McGraw-Hill, 2008.
 M. H. Sadd, Elasticity: Theory, Applications And Numerics, Elsevier, 2005.
 S. H. Crandall, N. C. Dahl and T. J. Lardner, An Introduction To The Mechanics of Solids, 2nd Ed., Tata McGraw Hill, 2008.
 S. P. Timoshenko, Strength Of Materials, Vols. 1 and 2, CBS Publishers, 1986.
 H. Shames and J. M. Pitarresi, Introduction To Solid Mechanics, Prentice Hall of India, 2003.
 A. C. Ugural and S. K. Fenster, Advanced Strength And Applied Elasticity, 3rd Ed., Prentice Hall, 1994.
 A. P. Boresi, R. J. Schmidt and O. M. Sidebottom, Advanced Mechanics Of Materials, 5th Ed., John Wiley, 1993.
 Y.C. Fung, Foundations of Solid Mechanics, Prentice-Hall, 1965