fem fea finite element

1. FINITE ELEMENT METHOD
Week # 1

2. Course Descriptions
formulation and calculation of the
finite element ma
Procedures and modeling in finite element
method /
/ stiffness matrices
for spring and basic structural e
trices
method of weighted res
lements
idua
/
ls / Galerkin finite
element method /
general element
interpolation functions
applications in
heat transfer, fluid and s
formula
olid mec
tio
ha
n /
nics
Week # 1

3. Objectives
:- to how does the FEM work
:- to the finite element equation
:- to the elements in problem modeling
:- to problem by using FE
introduce
formulate
create
solve
a
M
:- to the computer programs in sopply lving
various problems
Week # 1

4. Interesting Topics (1/2)
Introduction to Finite Element Method
Mathematical Preliminaries
Spring and Bar Element Stiffness Matrices
Analysis of Truss Structures
Beam Theory and Flexural Beam Element
W
W
W
W
W
Week # 1

5. Interesting Topics (2/2)
Weighted Residuals Method and
Galerkin Finite Element Method
Interpolation (Shape) Functions
Applications in Heat Transfer
Applications in Fluid Mechanics
Applications in Solid Mechanic
W
W
W
W
W s
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6. Grade Compositions
Homeworks 10 %
Program Testing 40 %
Mid-Term Examination 20 %
Final-Term Examination 30 %
Total 100 %
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W
W
W
Week # 1

7. Course Outlines (1/16)
Course Descriptions
Objectives
Interesting Topics
Course Outlines
Y
Y
Y
Y
Overviews (Week # 1)
Week # 1

8. Course Outlines (2/16)
Brief History and Recent Developments
Basic Idea & Basic Concepts
Applications of FEM
Advantages of FEM
Existing Computer Programs for FEM
Examples of Finite Element Analysis
Y
Y
Y
Y
Y
Y
Introduction to WeekFEM ( # 2)
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9. Course Outlines (3/16)
Vector Analysis
Matrix Operations
Linear Algebra
Calculus (Differentiation & Integration)
Numerical Integration (Gauss Quadrature)
Y
Y
Y
Y
Y
Mathematical Prelim Wi ena ekries ( # 3)
Week # 1

10. Course Outlines (4/16)
Elastic Spring System
Linear Spring Element
Elastic Bar and Truss Elements
Y
Y
Y
Spring and Bar Element Stiffness
Matrice Weeks ( # 4)
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11. Course Outlines (5/16)
Minimum (Stationary) Potential Energy
Introduction of Truss Structures
Nodal Equilibrium Equations
Y
Y
Y
Analysis of Truss Structures (Week # 5)
Week # 1

12. Course Outlines (6/16)
Transformation of Element
Direct Assembly of Global Stiffness Matrix
Applying Boundary Conditions and
Constraint Forces
Strain and Stress in Truss Element
Y
Y
Y
Y
Analysis of Truss Structures (Week # 6)
Week # 1

13. Course Outlines (7/16)
Introduction to Elementary Beam Theory
Flexure Element
Stiffness Matrix for Flexure Element
Element Load Vector
Work Equivalence for Distributed Loads
Flexural Element with Axial Loading
Y
Y
Y
Y
Y
Y
Beam Theory and Flexural Beam Element Week( # 7)
Week # 1

14. Course Outlines (8/16)
*** Mid-Term Examination ***
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15. Course Outlines (9/16)
Method of Weighted Residuals
Galerkin Finite Element Formulation
Y
Y
Weighted Residuals Method and Galerkin
Finite Element M Weeeth kod ( # 9)
Week # 1

16. Course Outlines (9/16)
Application of Galerkin FEM to Bar
and Beam Elements
Application to 1-D Heat Conduction
Y
Y
Weighted Residuals Method and Galerkin
Finite Element M Weeketho #d ( 10)
Week # 1

17. Course Outlines (10/16)
Compatibility and Completeness
Polynomial Forms : 1-D Elements
Polynomial Forms : 2-D and 3-D Elements
2-D Elements : 3-Node Triangular Elements
2-D Elements : 6-Node Triangular Elements
2-D El
Y
Y
Y
Y
Y
Y ements : 4-Node Rectangular Elements
2-D Elements : 8-Node Rectangular ElementsY
Interpolation (Shape) Functions (Week # 11)
Week # 1

18. Course Outlines (11/16)
1-D Conduction : Quadratic Element
1-D Conduction with Convection
Heat Transfer in 2-D
Y
Y
Y
Applications in Heat WT era eknsfe #r ( 12)
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19. Course Outlines (12/16)
Week # 1
Heat Transfer with Mass Transport
Axisymmetric Heat Transfer
Time Dependent Heat Transfer
Y
Y
Y
Applications in Heat WT era eknsfe #r ( 13)

20. Course Outlines (13/16)
Week # 1
Introduction
Incompressible Flow
Stream Function in 2-D Flow
Velocity Potential Function in 2-D Flow
Incompressible Viscous Flow
Y
Y
Y
Y
Y
Applications in Fluid Mechanics (Week # 14)

21. Course Outlines (15/16)
Week # 1
Introduction
Plane Stress and Plane Strain Problems
Y
Y
Applications in Solid Mechanics (Week # 15)

22. Course Outlines (15/16)
Week # 1
Isoparametric Formulation of Plane Element
3-D Stress Elements
Strain and Stress Computation
Y
Y
Y
Applications in Solid Mechanics (Week # 16)

23. Textbooks / Additional Reading
Hutton, D.V., (2004), Fundamentals of Finite Element
Analysis, International Ed., Mc-Graw Hill, Singapore
rd
Reddy, J.N., (2006), An Introduction to the Finite
Element Method, 3 Ed.,International Ed.,
Mc-Graw Hill, Singapore
nd
Chandrupatla, T.R. and Belegundu, A.D., (1997),
Introduction to Finite Elements in Engineering,
2 Ed., International Ed., Prentice-Hall, New Jersey
Week # 1