Transcript Sin título de diapositiva - Universidad de Cantabria

Engineering
Computation
Part 0
E. T. S. I. Caminos, Canales y Puertos
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Introduction
Objectives
1. Broad introduction to Numerical Methods for
engineering as a general and fundamental tool for all
engineering disciplines (numerical calculus,
numerical analysis, and probability & statistics).
2. Literacy in 2 higher-level programming tools widely
used in engineering for numerical methods and
graphics: Excel and MATLAB.
3. Illustrate and discuss how numerical methods are used
in engineering practice, industry, and research.
4. Show some applications of Numerical methods to
Civil Engineering
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Introduction
ENGCOMP Course outline
0. Spreadsheets (Excel) and MATLAB.
1. Approximation, errors, and precision; introduction to
numerical differentiation.
2. Roots of functions of one variable.
3. Simultaneous linear equations:
- tri-diagonal, LU decomposition, iterative solutions;
- norms, condition number, operation counting.
4. Introductory probability & statistics
5. Curve-fitting, regression, and cubic splines.
6. Numerical integration and differentiation.
7. Numerical solution of ODE’s.
8. Introduction to numerical solutions of PDE’s.
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Introduction
Why are Numerical Methods so widely used in Engineering?
 Engineers use mathematical modeling (equations and data)
to describe and predict behavior of systems.
 Closed-form (analytical) solutions are only possible and
complete for simple problems (geometry, properties, etc.).
 Digital computers are widely available, powerful, and
cheap.
 Powerful software packages are available (special or
general purpose).
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Introduction
Applications of Numerical Methods in Engineering?
• Structural/mechanical analysis, design, and behavior:
Buildings, dams, bridges, towers
Plants, assembly lines, machines
• Communication/power
Network simulation
Train and traffic networks
• Computational Fluid Dynamics (CFD):
Weather prediction
Groundwater & pollutant movement
Ocean circulation
Dam break and flood routing
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Introduction
Why study Numerical Methods?
Numerical Analysis is a Discipline:
 Need to understand concepts and theory
- Know what problems can be solved.
- Know what problems cannot be solved, or when
problems will be troublesome.
 Need to understand methods and techniques
- Know why methods work, or judge when they are
working.
- Be able to create or modify tools (software) as needed.
- Evaluate errors, convergence, and stability of
arithmetic approximations.
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Introduction
Why study Numerical Methods? (continued)
Use of Numerical Methods is an Art:
• Numerical methods are approximate.
• The most appropriate method(s) is not always obvious.
• Evaluating precision and accuracy is an essential part of
the process.
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Introduction
Instructor: Prof. Enrique Castillo
Escuela de Ingenieros de Caminos
Universidad de Cantabria
[email protected]
Office Hours: any time by appointment
Teaching Assistants :
Carmen Sordo
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PS office hours & grading
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Introduction
Computing Languages:
Spreadsheets
– Microsoft Excel (w/Visual Basic)
Numerical Languages
– MATLAB
Electronic Communication by e-mail:
• e-Mail with Eudora or Web Email
Computer assignments will be submitted as
attachments via e-mail: [email protected]
• Word, Excel, & MATLAB documents as enclosures
• documents will be distributed via the ENGCOMP web
page. http://personales.unican.es/castie/
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Introduction
ENGCOMP Course Materials
Required Textbook and Notes:
• Chapra & Canale, Numerical Methods for Engineers, 4th Ed., 2002
Recommended Texts:
• Palm, Introduction to MATLAB for Engineers.
• The MathWorks, The Student Edition of MATLAB.
• Pratap, Getting Started with MATLAB.
• Kuncicky, Introduction to EXCEL.
Will Distribute handouts via course web page, e.g.:
"Introduction to Spreadsheets: Using Microsoft EXCEL"
"Primer on MATLAB"
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Bibliography
– Chapra S. C., Canale R. P., “Métodos Numéricos para Ingenieros”, Mc. GrawHill,1999. Tercera Edición.
– Burden R. L., Raires J. D., “Análisis Numérico”. Ed. Grupo Editorial
Iberoamericana,1998. Sexta Edición.
– Kincaid D., Cheney W., “Análisis Numérico”. Addison-Wesley
Iberoamericana,1994.
– Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P., “Numerical Recipes
in C. The Art of Scientific Computing”. Cambridge University Press. Second
Edition.
– Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P., “Numerical Recipes
in C. Example Book (C)”. Cambridge University Press. Second Edition.
– Stoer J., Burlirsch R., “Introduction to Numerical Analysis”, Springer Verlag,
Berlin,1992.
– Michael T. Heat, “Scientific Computing: An Introductory Survey”, Ed. Mc Grawn
Hill.
– Gander W., et al. “Solving Problems in Scientific Computing using Maple and
Matlab”, Springer Verlag, Berlin,1993.
– Mathews, J. H., Kurtis D. F., “Métodos Numéricos con Matlab”, Prentice Hall
Iberia, D. L. 1999.
– Ottosen, N., Petersson H., “Introduction to the Finite Element Method”, Prentice
Hall, 1992.
– Herrero, H., Díaz Cano, A, “Informática Aplicada a las Ciencias y a la Ingeniería
con Matlab” , E. T. S. de Ingenieros Industriales. UCLM.
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Introduction
Weekly Assignments
• Problem Sets (PS) due Tuesday
- teams of 3; work together, check each other
- teams to be formed by F, October. 10
- first PS due on T, October. 10
• Computer Assignments (CA) due Friday
-
teams of 3; work together, learn from each other
submit electronically
first CA due next week (F, Oct. 10)
CA01 is on the ENGCOMP web page
• Assignment submissions must follows the standards
described on the course web page.
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Mathematical Models
Grades & Tentative Weighting (Letter Grade only):
Computer Assignments (CA)
20%
For 2 Prelims
40%
Final Exam
20%
Attendance & participation & various
20%
Because ENGCOMP serves to fulfill a College computing
requirement, to pass the course, you MUST pass all but one
Spreadsheet assignments and all but one MATLAB
assignments with a grade of C- or better.
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Mathematical Models
• Evening Preliminary exams:
Prelim 1: November 26, 16.00.
Prelim 2: To be anounced.
• Final exam
To be anounced
All exams will be open book.
Be sure to bring your textbook, notebook, pocket calculator,
and a writing implement to all exams.
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Introduction
Teams
• Objectives:
- To simulate professional practice, students will work in
teams when doing the homework and computer
assignments.
- Research shows it is advantageous for the teams to be of
mixed ability and for all team members to take
responsibility for the work and success of other team
members.
• Implementation:
- Teams will be organized freely or assigned by the Professor.
- All members of every team will be responsible for the
accuracy and completeness of the assignment and any
violations of academic integrity.
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Bridge crane design example
Bridge
girder
Design elements : top plate, bottom
plate, web, etc.
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Modes of failure
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Modes of failure
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Retaining wall example
Geometry: heel, stem and toe dimensions,
soil cover, etc.
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Retaining wall example (Failure Modes)
1. Sliding failure
2. Overturning failure
3. Bearing capacity
failure
4. Stem bending failure
5. Stem shear failure
6. Toe bending failure
7. Toe shear failure
8. Heel bending failure
9. Heel shear failure
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Vertical Breakwater
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Failure modes
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Failure modes
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Solution
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