Solid Mechanics
Solid Mechanics
Aspirants appearing for a Ph.D. Degree
All candidates will be tested on Basic Mathematics and Advanced
Mechanics of Solids. Apart from this the candidates can choose any two of
the following areas for the purpose of interview.
1. Computational Solid Mechanics
2. Experimental Solid Mechanics
3. Fracture Mechanics and Fatigue
4. Composite Materials and Structures
5. Plasticity and Smart Materials
Syllabus
Advanced Mechanics of Solids
Analysis of state of stress and strain at a point. – Differential equation of equilibrium of a deformable body
and strain displacement relations in Cartesian and Cylindrical co-ordinates. Generalized Hooke’s law.
Solution of Boundary Value Problems in a two-dimensional elastic continuum, St. Venant’s principle.
Specialization to problems of infinite domain, thick cylinders, Stress concentrations around holes,
specialization to problems of semi-infinite domains, Computation of contact stresses for two bodies in line
contact. Torsion of non-circular cross sections – Membrane analogy – hollow thin wall multiply connected
torsion members. Beam on elastic foundations – short beams. Theories of failure of ductile and brittle
materials, Yield criteria.
Suggested Text::
a. Srinath L.S., Advanced Mechanics of Solids, Tata McGraw-Hill, 1980
b. Boresi, A.P. and Sidebottom, O.M., Advanced Mechanics of Materials, John Wiley, 1993.
c. Timoshenko, S.P. and Goodier, J.B., Theory of Elasticity, McGraw-Hil Kogakusha Ltd., 1970
Computational Solid Mechanics
Types of differential equations and their exact solution procedures, Weighted residual methods in
engineering analysis, Finite Difference Methods, Application to time integration schemes in heat transfer,
anisotropic elasticity etc. Principle of minimum potential energy and complimentary potential energy,
Principle of virtual work and its application in Finite Element Method, Interpolation functions, Exact and
numerical integration schemes, Transformation of integral equations into algebraic equations, Solution of
algebraic equations and obtaining the field quantities, Introduction to simple finite elements, Modeling of
physical problems using FEM.
Suggested Text::
a. Reddy, J. N., Introduction to the Finite Element Method, McGraw-Hil , 1993.
b. Zienkiewicz, O. C. and Taylor, R. E., The Finite Element Method, Vol. I, 4th Ed., McGraw-Hil ,
New York, 1989.
c. Cook, R. D., Malkus, D. S. and Plesha, M. E., Concepts and Application of Finite Element
Methods, 3rd Ed., Wiley, New York, 1989.
Experimental Solid Mechanics
Electrical resistance strain gauges - Foil strain gauges, Stress gauge, - Rosette analysis - strain gauge
circuits - Theory of photoelasticity – Photoelastic coatings – Measurement of Force, torque, displacement,
Principles of Holography, Speckle and Moire, Measurement of residual stress.
Suggested Text:
a. Dally and Riley, Experimental Stress Analysis, 2nd Ed., McGraw-Hil , 1978.
b. Kobayashi,
A.
S.,
Handbook on Experimental Mechanics, SEM and VCH, 1993.
Fracture Mechanics and Fatigue
Linear elastic fracture mechanics, Stress intensity factor, Energy release rate, Relation between SIF and
energy release rate, Conditions for onset of crack growth, Fracture toughness testing, Crack growth and
fracture mechanisms, Modeling of plasticity effects, J-integral, Methods to evaluate SIF, Paris law, Crack
closure, Retardation models, Repair methodologies, Elasto-plastic fracture mechanics, Mixed-mode
fracture
.
Suggested Text:
a. Broek,
D.
Elementary Engineering Fracture Mechanics, 4th ed., Kluwer Academic,1986.
b. Anderson, T. L., Fracture Mechanics: Fundamentals and Applications, 3rd Ed., CRC Press, 2004.
c. Prashant
Kumar,
Elements of Fracture Mechanics, Wheeler Publishing,1999.
Composite Materials and Structures
Introduction to Composite Materials - Generalised Hooke's Law - Transformation of Elastic Constants –
Rule of mixtures - Structural Behaviour of Lamina - Classical Lamination Theory - Constitutive Relations -
Stress, Analysis of Laminated Plates and Shells - Interlaminar and Free Edge Stresses; Delamination
Criterion and Failure Theories - First and Higher Order Theories - Finite Element Method applied to
Laminated Composites.
Suggested Text:
a. Jones, R. M., Mechanics of Composite Materials, 2nd Ed., Taylor and Francis, 1999
b. Reddy, J. N., Mechanics of Laminated Composite Plates and Shells, CRC Press, 2004.
c. Agarwal, B. D., and Broutman, L. J., Ananlysis and Performance of Fiber Composites, J. Wiley.
Plasticity and Smart Materials
Yield and Failure criteria; experimental studies; physical mechanisms; uniaxial plasticity; Linear Elastic
Fracture Mechanics, Stress based and strain based fatigue of metals.
Smart technology, types of smart materials, underlying mechanisms and applications of smart materials
and structures.
Suggested Text:
1. Chen, W. F. and Han, D. J., Plasticity for Structural Engineering, Springer-Verlag Berlin, 1992
2. Chakrabarty,
Theory of Plasticity, McGraw-Hill Book Company, New York 1990
3. Suresh, S., Fatigue of Materials, 2nd Ed., Cambridge Univ. Press, 1998.
4. Gandhi, M.V. and Thomson, B.S., Smart Materials and Structures, Chapman & Hall, NY, 1992.
Aspirants appearing for a M.S. Degree
All candidates will be tested on Basic Mathematics and Mechanics of
Solids. Apart from this the candidates can choose any one of the following
areas for the purpose of interview.
1. Computational Solid Mechanics
2. Experimental Solid Mechanics
3. Fracture Mechanics and Fatigue
4. Composite Materials and Structures
5. Plasticity and Smart Materials
Syllabus
Mechanics of Solids
Equilibrium of rigid bodies, free body diagram, Analysis of beams and trusses, Equilibrium of continuous
systems -derivation of relation between load, shear force and bending moment. Energy conservation in
rigid bodies -potential energy and elastic energy. Virtual work in multibody assemblies. Equilibrium of
deformal\ble solids; Stress and Strain; Thin walled structures; Transformation of stress and strain tensors,
Engineering Materials and their properties; Axial Members; Torsion; Bending; Transverse Shear; Failure
Theories; Analysis for deflections and forces; Inelastic analysis; Buckling of columns
Suggested
Text:
a. Popov,
E.P.,
Engineering Mechanics of Solids, 2nd Ed., Prentice Hall India, 1998.
b. Crandall, S.H., Dahl, N.C. and Lardner, T.J., An Introduction to the Mechanics of Solids, 2nd
Ed., McGraw-Hil , 1978.
