# MEC 303 - FINITE ELEMENT METHODS by raghuadh

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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 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

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