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Finite Element Application

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Name 'finite element' was introduced in 1960 when triangular and rectangular ... Enter bottom left coordinates. Enter top right coordinates. Steps Con't ' ... – PowerPoint PPT presentation

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Title: Finite Element Application


1
Finite Element Application
  • Group 2
  • Mason Vance
  • Alex V. Dugé
  • Abdul-Razak Nuhu

2
AGENDA
  • Introduction
  • History of FEM
  • Overview of FEM theory
  • FEM Applications
  • Examples
  • Advantages of FEM
  • Conclusion
  • Bibliography

3
INTRODUCTION
  • What is finite element method?
  • -- An approximate method for solving partial
    differential equations by replacing
    continuous functions by piecewise
    approximations defined on polygons, which are
    referred to as elements.

4
HISTORY
  • Name finite element was introduced in 1960 when
    triangular and rectangular elements were used
    for plane stress analysis
  • Modern development started in the 1940s in
    structural engineering
  • Developed from Jacobian, Gauss, Jordan, and
    Seidel iteration
  • Used only for static analysis until 1965
  • Variational formulation became available in 1967
  • Uses matrix algorithm

5
Overview of FEM theory
  • Continuous field over the entire domain
  • Domain divided into subsections with finite
    degree of freedom

6
General Steps
  • Discretize the Domain
  • a. Divide the domain into finite element using
    appropriate element type
  • Select a Displacement Function
  • a. Define a function within each element using
    the nodal values
  • Define the temperature variation through the
    element
  • Derive the Element Stiffness Matrix and Equations

7
General Steps contd
  • Assemble the element equations to get the global
    equations
  • Apply Boundary Conditions
  • Solve for the unknowns degree of freedom
  • Solve for the nodal temperatures
  • Interpret the results

8
FEM in the Old Age
9
FEM in the Modern Age
10
FEM Application
  • Steady-state Heat transfer
  • Transient Heat transfer
  • Steady and Unsteady Fluid flow
  • Linear Transient Stress ( Direct integration)
  • Linear Transient Stress (Model Superposition)
  • Linear Response Spectrum (Model Superposition)
  • Linear Random Vibration (Model Superposition)
  • Linear Frequency Response
  • Linear Critical Buckling Load
  • Electrostatic Current and Voltage
  • Electrostatic Field Strength and Voltage

11
FEM Application Cont
  • Dynamic Design-Analysis Method(DDAM)
  • Accupak/VE Mode Shapes and Natural Frequencies
  • Linear Mode Shape and Natural Frequencies with
    Load

12
(No Transcript)
13
Step-by-step instructions on using Algor
  • Open Engineering folder
  • Select Algor FEA

14
Steps Cont
  • From here select Tools
  • From Tools initiate Superdraw

15
Steps Cont
  • Select the rectangle to begin drawing the plate

16
Steps Cont
  • Enter bottom left coordinates
  • Enter top right coordinates

17
Steps Cont
Enclose to bring plate into view
18
Steps Cont
  • Generate Mesh
  • Select appropriate units

19
Steps Cont
  • Choose yes
  • Select generate, then wait, OK, done

20
Steps Cont
  • Discretized into elements

21
Steps Cont
  • Boundary condition
  • Set values by box applying to edges

22
Define analysis type (steady-state heat
transfer) Click box under Element (2-D) Click
Box under Material (copper) Click box under
Data to specify thickness Click on Global
23
Steps Cont
  • Click boxes as shown
  • Run analysis from Model Data Control

24
Steps Cont
Set multipliers to 1
25
Steps Cont
  • Pick Results from Model Data Control

26
Temperature distribution from lab
27
ADVANTAGES OF FEM
  • Model irregularly shaped bodies
  • Handle general load conditions quite easily
  • Model bodies composed of several different
    materials
  • Handle unlimited numbers and boundary conditions
  • Vary the size of elements to make possible to use
    small element when necessary.

28
ADVANTAGES Cont
  • Alter finite element model relative easy and
    cheap
  • Include dynamic effects
  • Handle nonlinear behavior existing with large
    deformations and nonlinear materials.

29
CONCLUSION
  • FEM can be use for optimization
  • FEM can be use for engineering analysis
  • Very cost effective
  • Time saver

30
References
  • www.nature.com/nsu/020101/ 020101-2.html
  • www.bruneni.com/East/33-807.html
  • www.habanf.com/newsletter.htm
  • www.iei.ie/steps/seniorcycle/civil.html
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