ME2353 FINITE ELEMENT ANALYSIS Syllabus

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INTRODUCTION (Not for examination) 5
Solution to engineering problems – mathematical modeling – discrete and continuum
modeling – need for numerical methods of solution – relevance and scope of finite
element methods – engineering applications of FEA
UNIT I FINITE ELEMENT FORMULATION OF BOUNDARY VALUE
PROBLEMS 5+3
Weighted residual methods –general weighted residual statement – weak formulation of
the weighted residual statement –comparisons – piecewise continuous trial functionsexample
of a bar finite element –functional and differential forms – principle of stationary
total potential – Rayleigh Ritz method – piecewise continuous trial functions – finite
element method – application to bar element
UNIT II ONE DIMENSIONAL FINITE ELEMENT ANALYSIS 8+4
General form of total potential for 1-D applications – generic form of finite element
equations – linear bar element – quadratic element –nodal approximation – development
of shape functions – element matrices and vectors – example problems – extension to
plane truss– development of element equations – assembly – element connectivity –
global equations – solution methods –beam element – nodal approximation – shape
functions – element matrices and vectors – assembly – solution – example problems
UNIT III TWO DIMENSIONAL FINITE ELEMENT ANALYSIS 10+4
Introduction – approximation of geometry and field variable – 3 noded triangular
elements – four noded rectangular elements – higher order elements – generalized
coordinates approach to nodal approximations – difficulties – natural coordinates and
coordinate transformations – triangular and quadrilateral elements – iso-parametric
elements – structural mechanics applications in 2-dimensions – elasticity equations –
stress strain relations – plane problems of elasticity – element equations – assembly –
need for quadrature formule – transformations to natural coordinates – Gaussian
quadrature – example problems in plane stress, plane strain and axisymmetric
applications
UNIT IV DYNAMIC ANALYSIS USING FINITE ELEMENT METHOD 8+4
Introduction – vibrational problems – equations of motion based on weak form –
longitudinal vibration of bars – transverse vibration of beams – consistent mass matrices
– element equations –solution of eigenvalue problems – vector iteration methods –
normal modes – transient vibrations – modeling of damping – mode superposition
technique – direct integration methods
UNIT V APPLICATIONS IN HEAT TRANSFER & FLUID MECHANICS 6+3
One dimensional heat transfer element – application to one-dimensional heat transfer
problems- scalar variable problems in 2-Dimensions – Applications to heat transfer in 2-
Dimension – Application to problems in fluid mechanics in 2-D
L=42, T=18 TOTAL:60 PERIODS
TEXT BOOK:
1. P.Seshu, “Text Book of Finite Element Analysis”, Prentice-Hall of India Pvt. Ltd., New
Delhi, 2007. ISBN-978-203-2315-5
REFERENCES:
1. J.N.Reddy, “An Introduction to the Finite Element Method”, McGraw-Hill International
Editions(Engineering Mechanics Series), 1993. ISBN-0-07-051355-4
2. Chandrupatla & Belagundu, “Introduction to Finite Elements in Engineering”, 3rd
Edition, Prentice-Hall of India, Eastern Economy Editions. ISBN-978-81-203-2106-9
3. David V.Hutton,”Fundamentals of Finite Element Analysis”, Tata McGraw-Hill Edition
2005. ISBN-0-07-239536-2
4. Cook,Robert.D., Plesha,Michael.E & Witt,Robert.J. “Concepts and Applications of
Finite Element Analysis”,Wiley Student Edition, 2004. ISBN-10 81-265-1336-5