finite element week 1
TRANSCRIPT
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FINITE ELEMENT METHODWeek # 1
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Course Descriptions
formulation and calculation of thefinite element ma
Procedures and modeling in finite elementmethod /
/ stiffness matricesfor spring and basic structural e
trices
method of weighted reslements
idua /
ls / Galerkin finiteelement method / general element
interpolation functionsapplications in
heat transfer, fluid and s formula
olid mectio
han /
nics
Week # 1
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Objectives
:- to how does the FEM work:- to the finite element equation:- to the elements in problem modeling:- to problem by using FE
introduceformulatecreatesolvea
M:- to the computer programs in sopply lving various problems
Week # 1
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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
Week # 1
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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
s
Week # 1
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Grade Compositions
Homeworks 10 %
Program Testing 40 %
Mid-Term Examination 20 %
Final-Term Examination 30 %
Total 100 %
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Course Outlines (1/16)
Course Descriptions Objectives Interesting Topics Course Outlines
Overviews (Week # 1)
Week # 1
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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
Introduction to Week FEM ( # 2)
Week # 1
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Course Outlines (3/16)
Vector Analysis Matrix Operations Linear Algebra Calculus (Differentiation & Integration) Numerical Integration (Gauss Quadrature)
Mathematical Prelim Wi ena ekries ( # 3)
Week # 1
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Course Outlines (4/16)
Elastic Spring System Linear Spring Element Elastic Bar and Truss Elements
Spring and Bar Element StiffnessMatrice Weeks ( # 4)
Week # 1
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Course Outlines (5/16)
Minimum (Stationary) Potential Energy Introduction of Truss Structures Nodal Equilibrium Equations
Analysis of Truss Structures (Week # 5)
Week # 1
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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
Analysis of Truss Structures (Week # 6)
Week # 1
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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
Beam Theory and Flexural Beam Element Week ( # 7)
Week # 1
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Course Outlines (8/16)
*** Mid-Term Examination ***
Week # 1
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Course Outlines (9/16)
Method of Weighted Residuals Galerkin Finite Element Formulation
Weighted Residuals Method and GalerkinFinite Element M Weeeth k od ( # 9)
Week # 1
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Course Outlines (9/16)
Application of Galerkin FEM to Bar and Beam Elements
Application to 1-D Heat Conduction
Weighted Residuals Method and GalerkinFinite Element M Weeketho #d ( 10)
Week # 1
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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
ements : 4-Node Rectangular Elements
2-D Elements : 8-Node Rectangular Elements
Interpolation (Shape) Functions (Week # 11)
Week # 1
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Course Outlines (11/16)
1-D Conduction : Quadratic Element 1-D Conduction with Convection Heat Transfer in 2-D
Applications in Heat WT era eknsfe #r ( 12)
Week # 1
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Course Outlines (12/16) Week # 1
Heat Transfer with Mass Transport Axisymmetric Heat Transfer Time Dependent Heat Transfer
Applications in Heat WT era eknsfe #r ( 13)
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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
Applications in Fluid Mechanics (Week # 14)
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Course Outlines (15/16) Week # 1
Introduction Plane Stress and Plane Strain Problems
Applications in Solid Mechanics (Week # 15)
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Course Outlines (15/16) Week # 1
Isoparametric Formulation of Plane Element 3-D Stress Elements Strain and Stress Computation
Applications in Solid Mechanics (Week # 16)
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Textbooks / Additional Reading
Hutton, D.V., (2004), Fundamentals of Finite ElementAnalysis, International Ed., Mc-Graw Hill, Singapore
rd
Reddy, J.N., (2006), An Introduction to the FiniteElement 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