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!
2Introduction to Scientific Computing
- http//nm.MathForCollege.com
- Transforming Numerical Methods Education for STEM
Undergraduates
3My 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
4Why use Numerical Methods?
5Why use Numerical Methods?
- To solve problems that cannot be solved exactly
6Why use Numerical Methods?
- To solve problems that are intractable to solve
exactly!
7Steps in Solving anEngineering
Problemhttp//nm.MathForCollege.com
8How do we solve an engineering problem?
9Example of Solving an Engineering Problem
10Bascule Bridge THG
11Bascule Bridge THG
Hub
Trunnion
Girder
12Trunnion-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
13Problem
- After Cooling, the Trunnion Got Stuck in Hub
14Why did it get stuck?
- Magnitude of contraction needed in the trunnion
was 0.015 or more. Did it contract enough?
15Video of Assembly Process
Unplugged Version
VH1 Version
16Consultant calculations
17Is the formula used correct?
T(oF) a (µin/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
18The Correct Model Would Account for Varying
Thermal Expansion Coefficient
19Can You Roughly Estimate the Contraction?
Ta80oF Tc-108oF D12.363
20Can You Find a Better Estimate for the
Contraction?
Ta 80oF Tc -108oF D 12.363"
21Estimating Contraction Accurately
Change in diameter (?D) by cooling it in dry
ice/alcohol is given by
Ta 80oF Tc -108oF D 12.363"
22So 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.
23Revisiting 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
25Introduction to Numerical MethodsMathematical
Procedures
- http//nm.MathForCollege.com
26Mathematical 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
27Nonlinear Equations
How much of the floating ball is under water?
Diameter0.11m Specific Gravity0.6
28Nonlinear Equations
How much of the floating ball is under the water?
29Differentiation
What is the acceleration at t7 seconds?
30Differentiation
What is the acceleration at t7 seconds?
Time (s) 5 8 12
Vel (m/s) 106 177 600
31Simultaneous Linear Equations
Find the velocity profile, given
Time (s) 5 8 12
Vel (m/s) 106 177 600
Three simultaneous linear equations
32Interpolation
What is the velocity of the rocket at t7 seconds?
Time (s) 5 8 12
Vel (m/s) 106 177 600
33Regression
Thermal expansion coefficient data for cast steel
34Regression (cont)
35Integration
Finding the diametric contraction in a steel
shaft when dipped in liquid nitrogen.
36Ordinary Differential Equations
How long does it take a trunnion to cool down?
37Additional 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
39Passing 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