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

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

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.

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

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

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

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

FEM in the Old Age

FEM in the Modern Age

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

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

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

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

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

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

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

Steps Con’t Generate Mesh Select appropriate units

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

Steps Con’t Discretized into elements

Steps Con’t Boundary condition Set values by box applying to edges

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”

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

Steps Con’t Set multipliers to 1

Steps Con’t Pick “Results” from Model Data Control

Temperature distribution from lab

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.

ADVANTAGES Con’t Alter finite element model relative easy and cheap Include dynamic effects Handle nonlinear behavior existing with large deformations and nonlinear materials.

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

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