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KL college of Engineering (Autonomous)
MECHANICAL Department
III Year 8.Tech. (ME) First Semester 2010-11
COURSE HANDOUT
Course No
Course Title FINITE ELEMENT ANALYSIS
Course coordinator N:Ramesh
Course Instructors Dr.K.V.Ramana & P.Srikanth
Course Description :
This course provides an introduction to the finite element method, from engineering
rather than a purely mathematical point of view. However, the mathematical foundations
of the method are presented along with their physical interpretations. The basic theory
and several applications of the finite element method ..
Introduction to approximate solution methods for problems in elasticity; the RITZ
method; interpolation; weighted residual methods; applications of the finite element
method; isoparametric finite elements; displacement-based bending elements in solid
and structural mechanics; programming the finite element method; advanced topics in
finite element analysis
Scope and Objective:
In more and more engineering solutions today,we find that it is necessary to obtain
approximate numerical solutions to problems rather than exact closed form solutions.
The finite element method is a numerical analysis technique for obtaining
approximate solutions to a wide variety of engineering problems.
1. Understand the underlying principles of the finite element method:
2. Understand why the FEM works, its strengths and limitations;
3. Ability to formulate, implement and verify a finite element formulation for
engineering problems;
4. Understand the structure of a commercial FEM program.
Text Books
1. Introduction to Finite Elements in Engineering by Tirupathi R.Chandrupatla,
Prentice hall of India Pvt. Ltd, New Delhi-1
Reference book:
1. Finite Element Method by S.S.Rao
2. Finite Element Method by C.Krishna Murthy
UNIT-I
FUNDAMENTAL CONCEPTS: lntroduction, historical background, Analysis of 3-D
stresses & strains, stress strain relations, stress cubic, principle stress calculations,
potential energy and equilibrium, Stresses and Equilibrium, Rayleigh-Ritz method,
Galerkin method, Saint venant's principle, Von Mises stress.
UNIT -II
BASIC CONCEPTS OF F.E.M. AND ONE DIMENSIONAL PROBLEMS: Fundamental
concepts, Finite Element Modeling, Coordinates and Shape FunCtions, The Potential-
Ener.gy Approach, Galerkin Approach, Assemble of the Global Stiffness Matrix and
Load Vector, Properties of K, The Finite Element Equations; Treatment of Boundary
Conditions, Types of Boundary Conditions, Elimination Approach, Penalty Approach,
Penalty Approach.
ANALYSIS OF PLANE TRUSSES: Introduction, Plane Trusses, Local and Global
Coordinate Systems, , Element stiffness matrix, Stress Calculations. Examples of plane
Truss with three members.
UNIT -11/
TWO-DIMENSIONAL PROBLEMS USING CONSTANT STRAIN TRIANGLES:
Introduction, Finite Element Modeling, Constant-Strain Triangle (CST), Isoparametric
Representation, Potential-Energy Approach, Element Stiffness, Force Terms Stress
Calculations, Problem Modeling and Boundary Conditions. .
AXISYMMETRIC SOLIDS' SUBJECTED TO AXISYMMETRIC LOADING: Introduction,
Axisymmetric Formulation, Finite Element Modeling: Triangular Element, Potential-
Energy Approach, Body force Term, Stress Calculations; Problem modeling and
Boundary Conditions. .
SCALAR FIELD PROBLEMS: Introduction, Steady-State heat Transfer, One-
Dimensional Heat Conditions, governing equation, boundary conditions, the one
dimensional element.
DYNAMIC CONSIDERATIONS:lntroductiori, Formulation, Element Mass Matrices,
Evaluation of Eigen values and Eigenvectors; properties of Eigenvectors, Eigen value-
Eigenvector Evaluation for line only.
Lecture Chapter in
Learn.ing objectives . Topics to be provided
No. the text Book
1 Introduction to FEA T1 P 1
2 Introduction to 3-D state of stress T1 P 2-3
Normal and shear stresses on a inclined R1 P 9
3
plane
To get introduced to Normal and shear stresses on a inclined R1 P 5-9
4 the FEA process plane
Normal and shear stresses on a inclined T1 P 9
5
plane
6 Principal stresses and stress cubic CN'
7 Principal planes .. CN
8 Principal strains T1 P 7-9
9 To apply various Potential energy and equilibrium T1 P 9-11
numerical method for
10 Rayleigh Ritz method T1 P 11
FEA
11 Galerikin's method T1 P 12,CN
12 Saint Venant's principle, Von Mises stress T1 P 13
To apply various Problems on Galerikin's method& CN
13 numerical method for Rayleigh-Ritz
FEA Problems ow6alerikin's method& CN
14
Rayleigh-Ritz
UNIT-II
15 Assembly of global stiffness matrix T1 P 58
Finding globql
16 Properties of global stiffness matrix T1 P 61
stiffness matrix
17 Finite element equations T1 P 62
18 To analyze boundary Treatment of boundary conditions T1 P 63-71
cohclitTonfor various T1 P 63-71
19 examples Examples of axially loaded members
20 Introduction to plane trusses T1 P 103
21 Local and global coordinate system T1 P 104
22 Element stiffness matrix T1 P 106
23 To analyze plane Stress calculations T1 P 107
24 truss Plane truss with three mem,bers T1 P 114
25 Numericals on plane truss CN
26 Numericals on plane truss CN
27 Numericals on plane truss eN
UNIT-III
28 Introduction to 2-D problems CN
plane stress and plane strain and T1 P 187
29
modeling of 2-D element
~O Constant strain triangles T1 P 133
To analyze 2~D Isoparametric representation of & T1 P 130
31
problems analysis of 2-D element using potential
32 Evaluation of element stiffness and force T1 P 130,CN
Evaluation of 2-D element using CN
33
Galerikin's approach stress calculation
34 Treatment of boundary conditions CN
35 To analyze 2-D Numericals on plane stresses T1 P213-216
36 problems by using Numericals on plane strains T1 P 162
37 various elements Numericals using CST elements T1 P 162
UNIT-IV
38 Introduction to axisymmetric elements T1 P 162
39 Axisymmetric formulation 1:1 P 162
40 Fem using linear triangular elements T1 P 130
41 Problems on axisymmetry CN
42 To analyze Problems on axisymmetry CN
43 axisymetric problems Modeling of problems T1 P 152
44 Treatment of boundary conditions T1 P 152
45 Applications on axisymmetry T1 P 178
46 Numericals on solid cylinders T1 P 178-198
47 Numericals on hallow cylinders T1 P 178-198
48 Introduction to scalar field problems T1 P 306
T1 P 306
49 Introduction to scalar field problefT1s
To analyze scalar Steady state heat transfer, 1-D heat T1 P 308-330
50 field problems conduction, governing equation
51 .One dimensional scalar field problems T1 P 308-330
52 Functional approach for heat condition T1 P 308-330
UNIT-V
53 Introduction to formulation T1 P 367
54 Element mass matrices-"" T1 P 368
Evaluation of eigen values and eigen CN
55
To analyze Eigen vectors
56 values and Eigen Properties of eigen vectors T1 P 376
57 vectors Eigen-value and eigen vector evaluation T1 P 376
58 Treatment of transition element T1 P 404
59 Usaqe of plane 42 and plane 82 CN
60 revision CN
Evaluation Component _
.. Duration Weightage Date, Time & Venue
Assignment- I 40
Assignment -II 40 10
Home Assignments(3) -
Sessional -I 90
20
Sessional-II 90
Surprise tests(2) - 5
.'
Attendance 5
Comprehensive 3 hrs. 60
Total 100
SESSIONALS:
1. The Question 'paper consists of Three Se~tions.
2. The First Section has 7 Marks Question as per the Autonomous Exam
Pattern with internal choice and all Questions have to be answered.
3. The Second Section has 7 Marks Questions as per the Autonomous Exam
Pattern with internal choice and all Questions have to be answered.
4. The Third Section has 6 Marks Questions as per the Autonomous Exam
Pattern with internal choice and all Questions have to be answered
5. The Answer Scripts will be valued for 20 Marks and Marks will be awarded
accordingly as explained above.
2. Two Assignments will be conducted per semester. 75% weightage will be given
for the best one, 25% weightage will be given for the other one. Three home
assignments are also given in each semest~r.
3. Two Surprise tests will be conducted per semester. Best of two tests will be
considered 5 marks.
and evaluated for
Attendance will be considered for 5 marks. The demarcation is as follows:
95% and above 5 marks
90% and above 4 marks
85% and above 3 marks
80% and above 2 marks
75% and above 1 mark.
6. Notices
All notices regarding course matters will be displayed in both Notice-board and
e-Iearning site.
7. Tutorial
Tutorial will be conducted by the respective instructors. The tutorial is intended
to supplement the material taught in the lectures and practical solve problems and to
clear doubts. Class assignments, class test and other evaluation components will also e
conducted during tutorial. Students must actively participate in the tutorial andattenp
the class work with prior preparation.
N,D
COU RkcooRDI
L NATOR
