FINITE ELEMENT METHODWeek # 1

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

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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

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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

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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

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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Course Outlines (8/16)

*** Mid-Term Examination ***

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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)

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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)

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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)

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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)

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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)

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)

Course Outlines (15/16) Week # 1

Introduction Plane Stress and Plane Strain Problems

Applications in Solid Mechanics (Week # 15)

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)

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

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