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Welcome to EML3041: Computational Methods.

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Welcome to EML3041: Computational Methods. SIT IN FIRST FOUR ROWS ONLY My name is Dr. Kaw. Introduce yourself to the person on your left and right! – PowerPoint PPT presentation

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Title: Welcome to EML3041: Computational Methods.


1
  • Welcome to EML3041 Computational Methods.
  • SIT IN FIRST FOUR ROWS ONLY
  • My name is Dr. Kaw.
  • Introduce yourself to the person on your left and
    right! Say one thing (nothing personal) about
    yourself to them!
  • At home, go thru the piazza announcements.
  • All is well that ends well well-begun is
    half-done.
  • No cell phones, laptops or other distractions.
    Daydreamers and sleepers will not be disturbed!

2
Introduction to Scientific Computing
  • http//nm.MathForCollege.com
  • Transforming Numerical Methods Education for STEM
    Undergraduates

3
My advice
  • If you dont let a teacher know at what level you
    are by asking a question, or revealing your
    ignorance you will not learn or grow.
  • You cant pretend for long, for you will
    eventually be found out. Admission of ignorance
    is often the first step in our education.
  • Steven CoveySeven Habits of Highly Effective
    People

4
Why use Numerical Methods?
5
Why use Numerical Methods?
  • To solve problems that cannot be solved exactly

6
Why use Numerical Methods?
  • To solve problems that are intractable to solve
    exactly!

7
Steps in Solving anEngineering
Problemhttp//nm.MathForCollege.com
8
How do we solve an engineering problem?
9
Example of Solving an Engineering Problem
10
Bascule Bridge THG
11
Bascule Bridge THG
Hub
Trunnion
Girder
12
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
13
Problem
  • After Cooling, the Trunnion Got Stuck in Hub

14
Why did it get stuck?
  • Magnitude of contraction needed in the trunnion
    was 0.015 or more. Did it contract enough?

15
Video of Assembly Process
Unplugged Version
VH1 Version
16
Consultant calculations
17
Is the formula used correct?
T(oF) a (┬Áin/in/oF)
-340 2.45
-300 3.07
-220 4.08
-160 4.72
-80 5.43
0 6.00
40 6.24
80 6.47
18
The Correct Model Would Account for Varying
Thermal Expansion Coefficient
19
Can You Roughly Estimate the Contraction?
Ta80oF Tc-108oF D12.363
20
Can You Find a Better Estimate for the
Contraction?
Ta 80oF Tc -108oF D 12.363"
21
Estimating Contraction Accurately
Change in diameter (?D) by cooling it in dry
ice/alcohol is given by
Ta 80oF Tc -108oF D 12.363"
22
So what is the solution to the problem?
  • One solution is to immerse the trunnion in liquid
    nitrogen which has a boiling point of -321oF as
    opposed to the dry-ice/alcohol temperature of
    -108oF.

23
Revisiting steps to solve a problem
1) Problem Statement Trunnion got stuck in the
hub. 2) Modeling Developed a new model
3) Solution 1) Used trapezoidal rule OR b) Used
regression and integration. 4) Implementation
Cool the trunnion in liquid nitrogen.
24
  • THE END
  • http//nm.MathForCollege.com

25
Introduction to Numerical MethodsMathematical
Procedures
  • http//nm.MathForCollege.com

26
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 Transforms

27
Nonlinear Equations
How much of the floating ball is under water?
Diameter0.11m Specific Gravity0.6
28
Nonlinear Equations
How much of the floating ball is under the water?
29
Differentiation
What is the acceleration at t7 seconds?
30
Differentiation
What is the acceleration at t7 seconds?
Time (s) 5 8 12
Vel (m/s) 106 177 600
31
Simultaneous Linear Equations
Find the velocity profile, given
Time (s) 5 8 12
Vel (m/s) 106 177 600
Three simultaneous linear equations
32
Interpolation
What is the velocity of the rocket at t7 seconds?
Time (s) 5 8 12
Vel (m/s) 106 177 600
33
Regression
Thermal expansion coefficient data for cast steel
34
Regression (cont)
35
Integration
Finding the diametric contraction in a steel
shaft when dipped in liquid nitrogen.
36
Ordinary Differential Equations
How long does it take a trunnion to cool down?
37
Additional Resources
  • For all resources on this topic such as digital
    audiovisual lectures, primers, textbook chapters,
    multiple-choice tests, worksheets in MATLAB,
    MATHEMATICA, MathCad and MAPLE, blogs, related
    physical problems, please visit
  • http//nm.MathForCollege.com/topics/introduction_
    numerical.html

38
  • THE END
  • http//nm.MathForCollege.com

39
Passing this course
Tests Project HW Posts read
27 31 58 96
50 44 41 97
51 53 49 66
42 102 97 59
55 82 64 54
66 0 76 79
55 72 78 96
63 76 45 49
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