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ME 257 (JAN) 3:0 

Finite Element Methods 

Linear finite elements procedures in solid mechanics, convergence,isoparametric mapping and numerical Integration. Application of

finite element method to Poisson equation, calculus of variations,weighted residual methods, introduction of constraint equations by

Lagrange multipliers and penalty method, solution of linearalgebraic equations, application of finite element method to linear

elasto dynamics, solution of eigenvalue problems, modesuperposition and direct time integration algorithms, finite element

 programming.

Cook R. D., Malkus, D. S., and Plesha, M.E., Concepts andApplications of Finite Element Analysis, 3rd Edition, 1989.

Bathe, K. J., Finite Element Procedures 1982

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Materials and Structure Property Correlations

Atomic structure of materials, atomic bonding, crystal structure point, line and areal defects in crystal structure, dislocation concepts

of plastic deformation, critical resolved shear stress, interactions between dislocations and work hardening, fracture-microscopic

descriptions, strengthening. Mechanisms of metals, processingmaps, concepts of bio-materials. Natural and synthetics, fracture and

fatigue of bio-materials.

Raghavan, V., Materials Science and Engineers, Prentice Hall, 1979.

Davidge, R.W., Mechanical Behaviour of Ceramics, 1986.Reed-Hill, R.E. and Abbaschian, R., Physical Metallurgy Principles,

Ratner B.D., Hoffman ,A.S., Schoen F. J., Lemons, J. E.,Biomaterials Science- An introduction to Materials in Medicine.

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ME 237 (AUG/JAN) 3:0 

Mechanics of Microsystems 

An overview of micro-systems and micro-fabrication, mechanicsissues relevant to micro-systems, scaling laws, materials properties

and their role in micro-systems, lumped modeling of micro-systems.Coupled-simulations of multi-energy domain systems including

electrostatics-mechanical, electro-thermal, thermo-mechanical, piezoelectric-mechanical, fluidic issues such as squeezed-film

effects. Application of numerical techniques such as finite elementand boundary element methods in solving steady-state and transient

regimes. Case studies of selected micro-systems devices and

systems. Introduction to biomechanics at the small sizes.

Pre-requisite: Multi-variable calculus and numerical analysis. No

 prior background in micro-systems or mechanics is assumed.

Senturia, S.D., Microsystem Design, Kluwer Academic Publishers,

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ME 259 (AUG) 3:0 Nonlinear Finite Element Methods 

Fundamentals of finite deformation mechanics-kinematics; stress

measures; balance laws, objectivity principle. Newton-Raphson

 procedure. Finite element formulation for plasticity and nonlinear

elasticity. Stress update algorithms for plasticity. Finite element procedures for dynamic analysis; Explicit and implicit timeintegration. Finite element modelling of contact problems – Slide-

line methods and penalty approach; Adaptive finite element analysis – automatic mesh generation; error estimation, choice of new mesh,

transfer of state variables. Finite element programming.

Pre-requisite: ME 257 or equivalent

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K. J. Bathe, Finite Element Procedures, Prentice Hall of India, New

Delhi 1997O. C. Zienkiewicz and R. L. Taylor, The Finite Element Methods,

Vols. I and II, McGraw Hill, 1991T. Belytshko, W.K. Liu and B. Moran, Nonliner Finite Elements for

Continua and Structures, Wiley, 2000.

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ME 260 (AUG) 3:0 Topology Optimization 

Hierarchy in structural optimization: topology, shape, and size.

Michelle continua and truss/frame topology optimization. Design

 parameterization and material interpolation: ground structuremethod, homogenization-based method, density distribution, level-

set methods, peak function methods, phase-field methods. Numerical methods for topology optimization: optimality criteria

methods, convex linearization and method of moving asymptotes,dual algorithms, numerical issues in the implementation of topology

optimization algorithms, applications to multi-physics problems,compliant mechanisms and material microstructure design.

Manufacturing constraints, other advanced topics.

G K Ananthasuresh 

Pre-requisite: ME 256. Background in finite element analysis is preferred.

Bendsoe, M.P., and Sigmund, O., Topology Optimization: Theory,

Methods, and Applications, Springer, 2003.

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ME 261 (AUG) 3:0 

Engineering Mathematics 

Vector and tensor algebra: Sets, groups, rings and fields, vector

spaces, basis, inner products, linear transformations, spectraldecomposition, tensor algebra, similarity transformations, singular

value decomposition, QR and LU decomposition of matrices, vectorand tensor calculus, system of linear equations (Krylov solvers,

Gauss-Seidel), curvilinear coordinate transformations.

Ordinary and partial differential equations: Characterization ofODEs and PDEs, methods of solution, general solutions of linear

ODEs, special ODEs, Euler-Cauchy, Bessel’s and Legendre’sequations, Sturm-Liouville theory, critical points and their stability.

Complex analysis: Analytic functions, Cauchy-Riemann conditionsand conformal mapping. Special series and transforms: Laplace and

Fourier transforms, Fourier series, FFT algorithms, wavelettransforms.

Kryeyzig E, Advanced Engineering Mathematics, 9th Ed., Wiley

2006.M.D. Greenberg, Advanced Engineering Mathematics, 2nd Ed.,

Pearson, 1998. F. B. Hildebrand, Methods of AppliedMathematics, Prentice Hall.

Bender and Orszag, Advanced Mathematical Methods for Scientistsand Engineers, Springer.

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ME 242 (AUG) 3:0 

Solid Mechanics 

Analysis of stress, Analysis of strain, stress-strain relations, two-

dimensional elasticity problems, Airy stress functions in rectangular

and polar coordinates, axisymmetric problems, energy methods, St.

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Venant torsion, elastic wave propagation, elastic instability and

thermal stresses.

Fung, Y. C. ,Foundations of Solid Mechanics, Prentice Hall.Srinath. L. S., Advanced Mechanics of Solids, Tata McGraw Hill.

Sokolnikoff, I. S., Mathematical Theory of Elasticity, Prentice Hall.

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ME 253 (JAN) 3:0 

Vibrations of Plates and Shells 

Shell coordinates, infinitesimal distances in curved shells, equationsof motion for general shell structures using Hamilton’s principle.

Specialization to commonly occurring geometries, modeshapes and

resonances of flat plates, rings, cylindrical shells and spherical

shells. Rayleigh-Ritz and Galerkin methods for finding approximate

modeshapes. Forced response: response to various types of loads

(point forces, moments, moving loads), transient and harmonicloads. Combination of structures using receptance.

Pre-requisite: a full course in lumped system vibrations

Werner Soedel,Vibrations of plates and shells, S.S. Rao Vibrationsof continuous systems,

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ME 256 (JAN) 3:0 

Variational Methods and Structural Optimization

Calculus of variations: functionals, normed vector spaces, Gateaux

variation, Frechet differential, necessary conditions for an

extremum, Euler-Lagrange multiplier theorem, second variations

and sufficient conditions. Weak form of differential equations,

application of Euler-Lagrange equations for the analytical solution

of size optimization problems of bars and beams, topologyoptimization of trusses and beams applied to stiff structures and

compliant mechanisms. Material interpolation methods in design parameterization for topology optimization, optimization

formulations for structures and compliant mechanisms involvingmultiple energy domains and performance criteria. Essential

 background for Karush-Kuhn-Tucker conditions for multi-variable

optimization, numerical optimization algorithms and computer

 programs for practical implementation of size, shape and topology

optimization problems.

Smith, D.R., Variational Methods in Optimization, Dover

Publication, 1998.

Haftka, R.T., and Gurdal, Z., Elements of Structural Optimization,

Kluwer Academic Publishers, 1992.

Bendsoe, M.P., and Sigmund, O., Topology Optimization: Theory,Methods and Applications, Springer, 2003.

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CE 204N (AUG) 3:0

Solid Mechanics

Introduction to tensor algebra and calculus, indicial notation,

matrices of tensor components, change of basis formulae,

eigenvalues, Divergence theorem. Elementary measures of strain.

Lagrangian and Eulerian description of deformation. Deformationgradient, Polar decomposition theorem, Cauchy-Green and

Lagrangian strain tensors. Deformation of lines, areas and volumes.Infinitesimal strains. Infinitesimal strain-displacement relations in

cylindrical and spherical coordinates. Compatibility. Tractions, bodyforces, stress at a point, Cauchy's theorem. Piola-Kirchhoff stress

tensors. Momentum balance. Symmetry of the Cauchy stress tensor.St. Venant's Principle. Virtual Work. Green's solids, elastic strain

energy, generalized Hooke's Law, material symmetry, isotropic

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linear elasticity in Cartesian, cylindrical and spherical coordinates,

elastic moduli, plane stress, plane strain,. Navier's formulation. Airystress functions. Selected problems in elasticity. Kirchhoff's

uniqueness theorem, Betti-Maxwell reciprocal theorem, Principle ofstationary potential energy, Torsion in circular and non-circular

shafts and thin-walled tubes, warping. Pure bending of thinrectangular and circular plates, small deflection problems in laterally

loaded thin rectangular and circular plates. Outline of Mindlin plate

theory. Introduction to yield and plasticity.

Fung, Y. C. and Pin Tong, Classical and Computational Solid

Mechanics, World Scientific, 2001Boresi, A.P., and Lynn P.P., Elasticity in Engineering Mechanics,

Prentice Hall 1974.Theoretical Elasticity, A.E. Green and W. Zerna, 1968, Dover

Publications

…………………………………………………………………….CE 205N (AUG) 3:0

An Introduction to Finite Elements in Solid Mechanics

Concepts of the stiffness method. Energy principles. ContinuumBVP and their integral formulation. Variational methods: Raleigh-

Ritz, weighted residual methods, virtual work and weak

formulations. Finite element formulation of one, two and three

dimensional problems, Isoparametric formulation. Computational

aspects and applications

Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method:

Vol. 1 (The Basis), Butterworth-Heinemann, 2000.Cook R.D.. Malkus, D. S., Plesha and Witt, R.J., Concepts andApplications of Finite Element Analysis, Fourth edition, John Wiley

and Sons.…………………………………………………………………….

CE 210N (Jan) 3:0

Linear Structural Dynamics

An overview of continuous dynamical systems; principle of virtualwork; Hamilton’s principle; Lagrangian equations of motion;

equations of motion by Reynolds transport theorem; PDEs of motion

for taut strings; Euler-Bernoulli beams and Kirchhoff plates;solutions of governing PDEs through separation of variables;

orthonormal bases and eigenfunction expansions; Rayleigh-Ritz andweighted residual methods; finite element semi-discretizations of

continuous dynamical systems; semi-discrete MDOF systems andeigenvalue problems; modal dynamics and the notion of an SDOF

model; free and forced vibration responses; damped MDOF systems;

structures under support excitations; a brief overview of

eigensolution techniques; direct integration techniques including

Euler and Newmark-beta methods.

D Roy and G V Rao, 2012, Elements of Structural Dynamics: A New Perspective, John Wiley, New York.

L Meirovitch, 1984, Elements of Vibration Analysis, McGraw-Hill, New York.

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CE 211N (JAN) 3:0Stability of Structures

Analysis of beam columns. Stability functions. Behavior of ideal

columns. Bifurcation buckling and limit point instability.Mechanical models of stability. Static and dynamic formulations.

Energy methods. Finite element formulation. Lateral torsional

 buckling of beams. Buckling of frames. Imperfection sensitivity and

 post critical behavior. Buckling of beams on elastic foundations,

arches and plates. Thermal buckling. Inelastic buckling. Dynamic

analysis of stability. Parametric instabilities and stability under

nonconservative forces. Divergence and flutter.S P Timoshenko and J M Gere, 1963, Theory of elastic stability,McGraw Hill, London.

G J Simtses and D H Hodges, 2005, Fundamentals of structuralstability, Elsevier, Amsterdam.

J M T Thompson and G W Hunt, 1973, A general theory of elasticstability, John Wiley, London

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PROBABILISTIC METHODS IN CIVIL ENGINEERING (3:0)

Randomness, uncertainty, modeling uncertainty, engineering judgment, introduction to probability, measures of variability,

 probability theory, random variables, probability mass and densityfunctions, moments of distribution, Bayes theorem, Stationary

 processes, autocovariance functions, functions of random fields,sampling techniques, concepts of sampling, sampling plans,

decisions based on samplings. levels of reliability, loads and

resistances, reliability methods, first order second moment, (FOSM)

method, Hasofer-Lind approach, comparative discussion, simulation

methods, random number generation, decision making, branching,

use of fault tree and event tree analysis and examples in civilengineering.

Ang, A.H.-S. and Tang, W.H. (1975 and 1984). ProbabilityConcepts in Engineering Planning and Design, Vol. 1 and Vol.2 ,

Basic Principles, John Wiley, New York.

 Nathabandu T. Kottegoda and Renzo Rosso (1998) Statistics,Probability, and Reliability for Civil and Environmental Engineers,McGraw-Hill International edition.

Baecher, G.B. and Christian, J.T. (2003). Reliability and Statistics inGeotechnical Engineering,

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CE 235N (JAN) 3:0

Optimization Methods

Basic concepts, Kuhn-Tucker conditions, linear and nonlinear

 programming, treatment of discrete variables, stochastic

 programming,. Genetic algorithm, simulated annealing, Ant Colonyand Particle Swarm Optimization, Evolutionary algorithms,Applications to various engineering problems.

Arora, J.S. Introduction to Optimization, McGraw-Hill(Int.edition).1989.

Rao, S.S., Optimization: Theory and Applications. Wiley Eastern,1992

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Nonlinear FEM in Structural Engineering

Concept of material, geometric, and contact nonlinearities. Reviewof continuum mechanics: stress and strain measures; balance laws.

Review of continuum plasticity: rules for yield, flow, and hardening.Total Lagrangian and updated Lagrangian formulations for

geometrically nonlinear solid continua. FE formulations for inelasticsolids with linear/nonlinear strain-displacement relations. Thermo-

mechanical analysis. Problems of structural dynamics. General

solution techniques

Pre-requisite:: Background in FEM and solid mechanics

T Belytschko, W K Liu, B Moran, and K I Elkhodary, 2014,

 Nonlinear finite elements for continua and structures, 2nd Edition,Wiley, Chichester.

J N Reddy, 2004, An introduction to nonlinear finite elementanalysis, Oxford University Press, New Delhi.

W F Chen and D J Han, 2008, Plasticity for structural engineers, J

.Ross publishing / Cengage Learning, New Delhi.J Bonet, and R D Wood, 2008, Non-linear continuum mechanics forfinite element analysis, Cambridge University Press, Cambridge.

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AE 224 : Analysis & Design of Composite Structures (3:0)

Introduction to composite materials, concepts of isotropy vs.

anisotropy, composite micromechanics (effective stiffness/strength

 predictions, load-transfer mechanisms), Classical Lamination Plate

theory (CLPT), failure criteria, hygrothermal stresses, bending of

composite plates, analysis of sandwich plates, buckling analysis oflaminated composite plates, inter-laminar stresses, First Order Shear

Deformation Theory (FSDT), delamination models, compositetailoring and design issues, statics and elastic stability of initially

curved and twisted composite beams, design of laminates usingcarpet and AML plots, preliminary design of composite structures

for aerospace and automotive applications. Overview of currentresearch in composites.

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Gibson, R.F., Principles of Composite Material Mechanics, CRC

Press, 2nd Edition, 2007.Jones, R.M., Mechanics of Composite Materials, 2nd Edition,

Taylor & Francis, 2010 (Indian Print).Daniel, I.M., and Ishai O., Engineering Mechanics of Composite

Materials, Oxford University Press, 2nd Edition, 2005.Reddy, J.N., Mechanics of Laminated Composite Plates and Shells –

Theory and Analysis, CRC Press, 2nd Edition, 2004.

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AE 223 : Energy and Finite Element Methods (3:0)

Introduction to energy methods; concept of work and energy,

 principle of virtual work, principle of minimum potential energy,

Raleigh Ritz method, Hamilton principle. Introduction to variationalmethods, weak form of governing equation, weighted residual

method, introduction to finite elements, Galerkin finite elements,

least square finite elements; finite element method various element

formulations for metallic, and composite and smart composite

structures, isoparametric element formulation, numerical integration,concept of consistency, completeness and mesh locking problems,

finite element methods for structural dynamics and wave propagation, mass and damping matrix formulation, response

estimation through modal methods, direct time integration, implicitand explicit methods. Introducton to super convergent finite element

formulation and spectral finite elements.

Cook R.D, Malkus D.S. and Plesha M.E., Finite Element Analysis,

John Wiley & Sons, New York, 1995. Bathe K.J., Finite ElementProcedures, Prentice Hall, New York, 1996. Varadan V.K., Vinoy

K.J. and Gopalakrishnan S., Smart Material Systems and MEMS,John Wiley & Sons, UK, 2006. Gopalakrishnan S., Chakraborty A.

and Roy Mahapatra D., Spectral Finite Elements, Springer Verlag,

UK, 2008.

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AE 233 : Smart Materials and Structures (3:0)

Sensors and actuators. Piezoelectric, magnetostrictive, and

electrostrictive materials. Shape memory alloys, electrorheologicaland magnetorheological fluids. Modeling of smart materials and

structures. Review of composite plate theory, smart laminatedcomposites, active fiber composites, finite element modeling of

smart structures. Control aspects of smart structures. Structuralhealth monitoring. Damage modeling. Algorithms for inverse

 problems. Vibration and noise control. Shape control. MEMS.

Culshaw B., Smart Structures and Materials, Artech House, 1996.

Srinivasan A.V.V. and McFarl D.M., Smart Structures Analysis andDesign, Cambridge University Press, 2000. Inman D.J. and Farrar

C.R., Damage Prognosis, John Wiley and Sons, 2005.

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AE 230 : Aeroelasticity (3:0)

Static aeroelasticity, bending-torsion flutter of a wing, dynamic

response of a wing to gust and atmospheric turbulence, flutteridentification, aeroelastic control.

Wright J.R.and Cooper J.E., Introduction to Aircraft Aeroelasticity

and Loads, John Wiley, 2008.

Hodges D.H. and Alvin Pierce G., Introduction to Structural

Dynamics and Aeroelasticity, Cambridge University Press, 2002.

Fung Y.C., An Introduction to the Theory of Aeroelasticity, Doveredition, 2002.

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Bisplinghoff R.L., Ashley H. and Halfman R.L., Aeroelasticity,

Dover edition, 1996.

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AE 234 : Engineering Optimization (3:0)

Constrained and unconstrained minimization of linear and nonlinear

functions of one or more variables, necessary and sufficientconditions in optimization, KKT conditions, numerical methods in

unconstrained optimization, one dimensional search, steepestdescent and conjugate gradient methods, Newton and quasi-Newton

methods. Finite difference, analytical and automatic differentiation,linear programming, numerical methods for constrained

optimization, response surface methods in optimization, orthogonal

arrays, stochastic optimization methods.

Engineering Optimization: A Modern Approach, Universities Press,2010.

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AE 239 : Applied and Computational Mechanics (3:0)

An overview of the mechanics and physics of solids; topics from

linear algebra and functional analysis, analysis and computation

using ordinary and partial differential equations, analysis of finitedifference schemes; boundary value problem, variational method,

thermodynamic equilibrium, system stability. Mathematicalfoundation of finite element method. Concepts of space-time

discretization and decoupling. Numerical error, numericalconvergence and numerical stability, ID, 2D and 3D finite element

formulation, analysis with examples, two and three-dimensionalfinite element formulations, analysis with examples. Computer

algorithm and computer code writing practices.

Lebedev L.P. and Vorovich I.I., Functional Analysis in Mechanics,

Springer Monograph in Mathematics, 2003. Reddy J.N., AnIntroduction to the Finite Element Method, McGraw Hill, 2005.

Susanne C.Brenner and Ridgway Scott L., The MathematicalTheory of Finite Element Methods, Springer 2002. James Demmel,

Applied Numerical Linear Algebra, SIAM, 1997.

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AE 240 : Modal Analysis: Theory and Applications (3:0)

Introduction to modal testing and applications. Frequency response

function (FRF) measurement. Properties of FRF data for SDOF andMDOF systems. Signal and System analysis. Modal analysis of

rotating structures. Exciters, sensors application in modal parameter

(Natural frequency, damping and mode shape) estimation. Vibrationstandards for human and machines. Calibration and sensitivity

analysis in modal testing. Modal parameter estimation methods.

Global modal analysis methods in time and frequency domain.

Derivation of mathematical models- modal model, response model

and spatial models. Coupled and modified structure analysis.Application of modal analysis to practical structures and condition

health monitoring.

Ewins D.J., Modal analysis: Theory and Practice, Research Studies

Press Ltd., England, 2000. Clarence W de Silva, Vibration:

Fundamentals and Practice, CRC press, New York, 1999. KennethG. McConnel, Vibration testing: Theory and Practice, John Wiley &

Sons Inc., New York, 1995.

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AE 360 : Nonlinear Mechanics of Composite Structures (3:0)

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Introduction to classical geometrical and physical non-linearities and

non-classical geometro-physical non-linearities in structuralmechanics. Mechanics of composite lamina and laminates including

response and failure as affected by nonlinearities. Variationalasymptotic methods of constructing nonlinear composite beam, plate

and shell theories. Non-classical effects resulting from non-linearities. Effects of non-linearities on stability of thin-walled

structures. Introduction to nonlinear finite element analysis

including mixed formulations. Applications to engineering

structures like pipes, springs and rotor blades.

Hodges D.H., Nonlinear Composites Beam Theory, Progress in

Astronautics & Aeronautics, Series 213, AIAA, 2006.

Berdichevsky V.L., Variational Principles of Continuum Mechanics,

I. Fundamentals & II.

Applications Interaction of Mechanics & Mathematics Series,

Springer, 2009.Current literature (International Journal of Nonlinear MechanicsInternational Journal of Solids and Structures etc.).

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AE 211 : Mathematics for Aerospace Engineers (3:0)

Real Analysis: Series and sequences, limits, continuity and

derivatives of functions, closed and open sets, compactness, metric

spaces, uniform convergence. Convex Analysis: Algebra of convexsets, convex functions and their properties. Linear Algebra:

Algebraic structures, vector spaces, linear transformations, canonical

forms, solution of linear systems of equations, techniques forEigenvalue extraction, iterative solvers. Introduction to variational

calculus: Weighted residual technique, numerical integration,integral transforms, solution of differential and partial differential

equations using integral transforms. Introduction to PartialDifferential Equations (PDE), linear convection (First order wave)

equation, method of characteristics. Non-linear convection equation

(Burgers equation): Discontinuous solutions and expansion waves,Riemann problem, Hyperbolic Systems of PDEs, Parabolic PDEs,

Elliptic PDEs.

David Logan J., An Introduction to Nonlinear PDEs, 2nd edition,Wiley Interscience. Courant R.and Hilbert D., Methods of

Mathematical Physics, Wiley-VCH. Gilbert Strang, Introduction toApplied Mathematics, Wellesley Cambridge Press.

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AE 221 : Flight Vehicle Structures (3:0)

Characteristics of aircraft structures and materials, introduction to

elasticity, torsion, bending and flexural shear, flexural shear flow inthin-walled sections, elastic bucking, failure theories. Variational

 principles and energy methods, analysis of composite laminates,loads on aircraft, basic aeroelasticity.

Sun, C.T., Mechanics of Aircraft Structures, John Wiley and Sons,

 New York, 2006.Megson, T.H.G., Aircraft Structures for Engineering Students,

Butterworth-Heinemann, Oxford, 1999.Wallerstein, D.V., Variational Approach to Structural Analysis, John

Wiley and Sons, 2001.

Shames, I.H., and Dym, C.L., Energy and Finite Element Methodsin Structural Mechanics, Taylor and Francis, 1991.

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