DEPARTMENT OF MECHANICAL ENGINEERING
FINITE ELEMENT METHODS
Sub Code
10ME64
IA Marks
Hrs/Week
04
Exam Hours
Total Hrs.
52
Exam Marks
:
:
:
25
03
100
Course Type: Program Core
PART-A
UNIT-1
Introduction: Equilibrium equations in elasticity subjected to body force, traction forces, and stress-strain relations
for plane stress and plane strains. General description of Finite Element Method, Application and limitations. Types
of elements based on geometry. Node numbering, Half band width.
07 Hrs
UNIT-2
Basic Procedure: Euler - Lagrauge equation for bar, beam (cantilever / simply supported fixed) Principle of virtual
work, principle of minimum potential energy, Raleighs Ritz method. Direct approach for stiffness matrix formulation
of bar element. Galerkins method.
07 Hrs
UNIT-3
Interpolation Models: Interpolation polynomials- Linear, quadratic and cubic. Simplex complex and multiplex
elements. 2D PASCALs triangle. CST elements-Shape functions and Nodal load vector, Strain displacement matrix
and Jacobian for triangular and rectangular element.
07 Hrs
UNIT-4
Solution of 1-D Bars: Solutions of bars and stepped bars for displacements, reactions and stresses by using penalty
approach and elimination approach. Guass-elimination technique.
06 Hrs
PART-B
UNIT-5
Higher Order Elements:Langranges interpolation, Higher order one dimensional elements-Quadratic and cubic
element and their shape functions. Shape function of 2-D quadrilateral element-linear, quadric element Isoparametric, Sub parametric and Super parametric elements. numerical integration : 1, 2 and 3 gauge point for 1D
and 2D cases.
06 Hrs
UNIT-6
Trusses: Stiffness matrix of Truss element. Numerical problems.
Hrs
06
UNIT-7
Beams:Hermite shape functions for beam element, Derivation of stiffness matrix. Numerical problems of beams
carrying concentrated, UDL and linearly varying loads.
06 Hrs
UNIT-8
Heat Transfer: Steady state heat transfer, 1D heat conduction governing equations. Functional approach for heat
conduction. Galerkins approach for heat conduction. 1D heat transfer in thin fins.
07 Hrs
SRI VENKATESHWARA COLLEGE OF ENGINEERING, BENGALURU
DEPARTMENT OF MECHANICAL ENGINEERING
Subject Overview:
Introduction to virtual simulation, verification and validation; Modeling and design through simulation based
predictive analysis; Numerical Methods; Finite Elements and their role in Engineering; Conceptual, preliminary and
detailed designs; 1-D models and comparison to analytical solutions in Stress analysis and heat conduction; Finite
elements for bars, beams in general 3-dimensional space; Weighted residual methods and variation methods; two
dimensional finite elements with triangles and quadrilateral elements; Iso parametric formulations; Applications to
Engineering analysis; extensions to axisymmetric and three-dimensional finite elements for engineering
computations; modeling issues, loads and boundary conditions.
Course Objectives:
1. Become familiar with the use and evaluation of numerical techniques with regards to applicability,
verification and validation through convergence and stability.
2. Use finite element techniques for analysis and leading to simulation based predictive design
3. Gain experience in defining and solving problems through home works and computer implementation of
numerical developments
4. Compare results with analytic and other numerical and/or experimental results as available for simple
problems.
Course Outcomes:
1. Understanding of numerical methods enabling obtaining solutions to problems with complex geometries
and boundary conditions and loads.
2. Ability to obtain useful convergent results as solutions to engineering problems which otherwise are not
easily tractable via analytic solutions.
3. Awareness of finite element advantages, limitations and applications.
4. Experience in numerical analysis for design.
5. Practical experience in applying the theory and numerical skills learned in the course to a variety of
engineering problems.
Prerequisite: Mathematics, Mechanics of materials, Heat and mass transfer
TEXT BOOKS:
1.
2.
Finite Elements in Engineering, T.R.Chandrupatla, A.D Belegunde, 3rd Ed PHI.
Finite Element Method in Engineering, S.S. Rao, 4th Edition, Elsevier, 2006.
REFERENCE BOOKS:
1.
2.
Finite Element Methods for Engineers U.S. Dixit, Cengage Learning, 2009
Concepts and applications of Finite Element Analysis, R.D. Cook D.S Maltus, M.E Plesha, R.J.Witt, Wiley
4th Ed, 2009
3.
Finite Element Methods, Daryl. L. Logon, Thomson Learning 3rd edition, 2001.
4.
Finite Element Method, J.N.Reddy, McGraw -Hill International Edition.
SRI VENKATESHWARA COLLEGE OF ENGINEERING, BENGALURU
DEPARTMENT OF MECHANICAL ENGINEERING
SRI VENKATESHWARA COLLEGE OF ENGINEERING, BENGALURU
DEPARTMENT OF MECHANICAL ENGINEERING
Course Delivery:
The Course will be delivered through lectures, class room interaction and group discussion.
Course Assessment and Evaluation:
IA
To whom
Internal
assessment
tests
Students
SEE
Direct Assessment
Methods
What
Semester end
examination
When/
Where
(Frequency
in the
course)
Max
marks
Evidence
collected
Contributing
to Course
Outcomes
Thrice(Avera
ge of the
best two will
be
computed)
25
Blue books
1,2,3,4,5
End of
course
(Answering
5 of
8 questions)
100
Marks list and
question
paper
1,2,3,4,5
ÐICAL PROFESSIONAL
DIFFERENTIAL APPLY MULTIVARIATE
EQUATIONS
CALCULUS AND
Experience in numerical analysis for design.
TOOLSMODERN ENGINEERING
and applications.
ISSUESCONTEMPORARY
Awareness of finite element advantages, limitations
LIFELONG LEARNING
are not easily tractable via analytic solutions.
ENGINEERING IMPACT OF
solutions to engineering problems which otherwise
EFFECTIVELYCOMMUNICATE
Ability to obtain useful convergent results as
E
& SOLVE ENGG. PROB.IDENTIFY, FORMULATE
geometries and boundary conditions and loads.
D
MULTIDISCIPLINARY FUNCTION ON
obtaining solutions to problems with complex
C
COMPONENTDESIGN A SYSTEM
Understanding of numerical methods enabling
B
EXPERIMENTSDESIGN & CONDUCT
COURSE OUTCOMES (CO'S)
A
& ENGINEERINGAPPLY MATHS, SCIENCE
Mapping Course Outcomes with Program Outcomes:
Practical experience in applying the theory and
numerical skills learned in the course to a variety
of engineering problems.
DEGREE OF COMPLIANCE L: LOW
M: MEDIUM
H:HIGH
SRI VENKATESHWARA COLLEGE OF ENGINEERING, BENGALURU
DEPARTMENT OF MECHANICAL ENGINEERING
SRI VENKATESHWARA COLLEGE OF ENGINEERING, BENGALURU
