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 domainx y
80°
Continuous field over the entire domain
Domain divided into subsections with finite degree of freedom x y
80°

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 cont’d
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 Con’t Dynamic Design-Analysis Method(DDAM)
Accupak/VE Mode Shapes and Natural Frequencies
Linear Mode Shape and Natural Frequencies with Load

13. Step-by-step instructions on using Algor
Open Engineering folder
Select Algor FEA

14. Steps Con’t
From here select “Tools”
From Tools initiate Superdraw

15. Steps Con’t
Select the rectangle to begin drawing the plate

16. Steps Con’t
Enter bottom left coordinates
Enter top right coordinates

17. Steps Con’t
“Enclose” to bring plate into view

18. Steps Con’t
Generate Mesh
Select appropriate units

19. Steps Con’t
Choose yes
Select generate, then wait, OK, done

20. Steps Con’t
Discretized into elements

21. Steps Con’t
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 Con’t Run analysis from “Model Data Control”
Click boxes as shown
Run analysis from “Model Data Control”

24. Steps Con’t
Set multipliers to 1

25. Steps Con’t
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 Con’t 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