Transcript Slide 1

FE Course Lecture II – Outline
UCSD - 10/09/03
1. Review of Last Lecture (I)
•
•
•
•
•
Formal Definition of FE:
Basic FE Concepts
Basic FE Illustration
Some Examples of the Second Order Equations in 1Dimension
Some Examples of the Poisson Equation – . (ku) = f
and Some Examples of Coupled Systems
2. Intro to 1-Dimensional FEs [Beams and Bars].
1. Fluid Mechanics Problem
2. Heat Transfer (Thermal) Problem
3. Beam/Bar problem
Finite Elements Principles and
Practices - Fall 03
1-Dimensional Finite Elements
1. Stiffness and Load Vector Formulations for mechanical, heat
transfer and fluid flow problems.
The system equation to be solved can be written in matrix form as:
[K] {D} = {q}
Where
[K] is traditional known as the ‘stiffness’ or ‘coefficient’ matrix
(conductance matrix for heat transfer, flow-resistance matrix for
fluid flow),
{D} is the displacement (or temperature, or velocity) vector and
{q} is the force (or thermal load, or pressure gradient) vector.
Finite Elements Principles and
Practices - Fall 03
A) For heat transfer problem in 1-dimensional, we have:
fx = -Kdt/dx [Fourier Heat Conduction Equation]
Q = -KAdt/dx (where Q=A fx)
[KT}{T} = {Q} [applicable for steady-state heat transfer problems]
kA  1  1  T1    q1 
L  1 1  T  q 
 2  2
Tbase=100oC
1
Tamb=20oC
5 5
Finite Elements Principles and
Practices - Fall 03
B) For fluid flow problem in 1-dimensional, we have:
md2u/dy2 – dp/dx = 0
[KF}{u} = {P} [applicable for steady-state flow problems]. P – pressure
gradient
 1  u1   q1 
    
L  1 1  u  q 
 2  2
m  1
Finite Elements Principles and
Practices - Fall 03
C) For stress problem in 1-dimensional, we have:
kd2u/dx2 – q = 0
[KF}{u} = {F}. F – joint force.
EA  1 1  d1    q1 
L 1 1  d  q 
 2  2
u=uo = 0
How about for a tube under pure torsion? How will the
coefficients look like?
Finite Elements Principles and
Practices - Fall 03
Review of Analysis Results. E.g., stress distribution. Exact Vs FE
solution. Error Estimation.
SOFTWARE-Specific Session:
Intro to software-specific issues. h-elements, p-Elements,
adoptive meshing.
Build 1D problem on ANSYS. Go through all steps.
Thermal problem on ANSYS
Bar problem on ANSYS
Flow problem on ANSYS/FEMLAB.
Homework 1 and Reading Assignments.
Finite Elements Principles and
Practices - Fall 03