Finite Element Application

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Finite Element Application

• Group 2
• Mason Vance
• Alex V. Dugé
• Abdul-Razak Nuhu

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AGENDA

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

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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.

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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

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Overview of FEM theory

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

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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

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General Steps contd

1. Assemble the element equations to get the global
   equations
2. Apply Boundary Conditions
3. Solve for the unknowns degree of freedom
4. Solve for the nodal temperatures
5. Interpret the results

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FEM in the Old Age
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FEM in the Modern Age
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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

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FEM Application Cont

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

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Step-by-step instructions on using Algor

• Open Engineering folder

• Select Algor FEA

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Steps Cont

• From here select Tools

• From Tools initiate Superdraw

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Steps Cont

• Select the rectangle to begin drawing the plate

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Steps Cont

• Enter bottom left coordinates

• Enter top right coordinates

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Steps Cont
Enclose to bring plate into view
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Steps Cont

• Generate Mesh

• Select appropriate units

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Steps Cont

• Choose yes

• Select generate, then wait, OK, done

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Steps Cont

• Discretized into elements

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Steps Cont

• Boundary condition

• Set values by box applying to edges

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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
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Steps Cont

• Click boxes as shown

• Run analysis from Model Data Control

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Steps Cont
Set multipliers to 1
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Steps Cont

• Pick Results from Model Data Control

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Temperature distribution from lab
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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.

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ADVANTAGES Cont

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

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CONCLUSION

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

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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