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Welcome to EML3041

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If you don't let a teacher know at what level you are by asking a question, or ... VH1 Version. http://numericalmethods.eng.usf.edu. 12. Consultant calculations ... – PowerPoint PPT presentation

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Title: Welcome to EML3041


1
Welcome to EML3041
2
My Advice but Quoting Someone Else
  • If you don't let a teacher know at what level you
    are by asking a question, or revealing your
    ignorance you will not learn or grow.
  • You can't pretend for long, for you will
    eventually be found out. Admission of ignorance
    is often the first step in our education.
  • Steven Covey - Seven Habits of Highly Effective
    People

3
No cell phone in my class
  • The fate of a cell phone ringing

4
EML 3041
  • Computational Methods
  • Spring 2009
  • Dr. Autar Kaw

5
How do we solve an engineering problem?
6
BRIDGEof LIONS (1927)
7
Bascule Bridge THG
8
Bascule Bridge THG
Hub
Trunnion
Girder
9
Trunnion-Hub-Girder Assembly Procedure
Step1. Trunnion immersed in dry-ice/alcohol Step2.
Trunnion warm-up in hub Step3. Trunnion-Hub
immersed in dry-ice/alcohol Step4. Trunnion-Hub
warm-up into girder
10
Problem
  • Trunnion Stuck in Hub
  • Venetian Causeway Bridge

11
Video of Assembly Process
Unplugged Version
VH1 Version
12
Consultant calculations
Clearance needed was 0.015 or more
13
Thermal Expansion Coefficient Variation with
Temperature
14
Roughly estimate the contraction using
trapezoidal rule
Ta80oF Tc-108oF D12.363
15
Estimating Contraction Accurately
Change in diameter (?D) by cooling it in dry
ice/alcohol is given by
Ta80oF Tc-108oF D12.363"
?D -0.0137"
16
Revisiting steps to solve a problem
1) Problem Statement Trunnion getting stuck into
the hub. 2) Modeling Developed the current model
for diametric contraction of the trunnion,
3) Solution We solved the model by using
regression and integration.
4) Implementation We solved existing problem by
cooling the trunnion in liquid nitrogen.
17
Mathematical Procedures
  • Nonlinear Equations
  • Differentiation
  • Simultaneous Linear Equations
  • Curve Fitting
  • Interpolation
  • Regression
  • Integration
  • Ordinary Differential Equations
  • Other Advanced Mathematical Procedures
  • Partial Differential Equations
  • Optimization
  • Fast Fourier Transform

18
Nonlinear Equations
Floating Ball Problem
19
Differentiation
Velocity vs. time rocket problem
What is the acceleration at t10 seconds?
20
Simultaneous Linear Equations
Find the velocity profile from
Three simultaneous linear equations
21
Interpolation
What is the velocity of the rocket at t10
seconds?
22
Regression
Thermal expansion coefficient data for cast steel
Regression is used to curve fit the data.
23
Regression (cont)
24
Integration
Finding the contraction in a trunnion
25
Ordinary Differential Equations
How long does it take the trunnion to cool down?
26
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