MA6735 - Continuum Mechanics (Spring 2008)

Mon. and Wed. 5:30-6:45; CU641

Lynn S. Bennethum

Office: CU 638, Phone 303-556-4810

Office hours: Mon, 4-5:15pm,. and Mon and Wed. after class in CU 638, or by appointment.

e-mail: Lynn.Bennethum@cudenver.edu

home page: http://www-math.cudenver.edu/~bennethm

fax: 303-556-8550

home phone: 303-683-6983 (Please call after 9am and before 9:30pm - about half the time I work at home on Fridays)
 

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Textbook: General Continuum Mechanics by T.J. Chung, 2007, Cambridge Univ. Press;  ISBN 978-0-521-87406-9.


Prerequisite: Linear Algebra (3191), ODE (3200), and a PDE class or familiarity with governing equations for a Newtonian fluid and/or elastic solid.

Goal of the Course:   There are several tools one can use to model physical processes.  At the molecular scale, molecular dynamics might be the appropriate tool.  Continuum Mechanics is the modeling of materials at the continuum scale - i.e. at a scale large enough that molecules are not distinguishable.  This is the scale used to describe solid deformation of materials or the flow of fluids.  At larger scales, randomness might play a role (for example, the flow of water through a dry heterogeneous soil) and in this case a stochastic approach might be more appropriate.   Typically continuous modeling of materials is valid from scales on the order of centimeters to meters. The goal of this course is to give you a broad base in continuous modeling, so that you have the knowledge to read and learn about specific models in particular areas.  The end-of-the-semester project is an opportunity for you to investigate models of particular materials in more detail, or you can investigate more mathematical topics within continuum mechanics.

Grading:

Homework

40%

Midterm

40%

Final Project

40%

 The worst 20% will be dropped (i.e. your worst score will be worth half of your other scores).

Homework:  I will be assigning homework periodically and it will be due 2-3 classes after being handed out.

Midterm:  There will be an in-class exam over the material covered during the first half of the semester.  You will be expected to know definitions and to manipulate vector equations in indicial notation.

Final Project:  I will be supplying a list of projects from which you may choose, or you may suggest one of your own. For most projects I will be able to give you some references. These projects are to be done individually. A written report will need to be turned in, and you will need to present your work to the class during the last month of classes.

References:  Besides the optional textbook, you may want to examine the following resources.  Please let me know if you find other resources which might be applicable.

 

  1. Eringen, A. Cemal,  Mechanics of Continua, New York, Wiley, 1967
                This is the text I will be most closely following.  Unfortunately it is out of print.  It is available at the Auraria library, and I have a copy.  Iif you find you are having difficulties with a particular topic, you may want to photocopy the appropriate sections.  This text is rather terse, but it makes an excellent reference book as it covers a wide range of topics.  It was one of the first texts which combined classical continuum mechanics with thermodynamics (entropy inequality).

 

  1. Hopman, T., Introduction to Indicial Notation.  Available online: http://www.uoguelph.ca/%7Ebvandere/indicial2.pdf  .  A brief common-sense introduction to indicial notation.

 

 

3.       Kennett, B. L. N., Introduction to Continuum Mechanics.  Available on the web at Samizdat Press.  This is a more traditional text (no thermodynamics) written from an engineering perspective.  It is clear and gives physical examples for motivation.  There is no discussion on indicial notation.  This would be a good reference for many projects.

 

4.      Backus, G., Continuum Mechanics.  Available on the web at Samizdat Press.
           This is very mathematical, proving all theorems rigorously.  The first half of the text gives notation and proves the Polar Identity (generalization of the delta-epsilon identity), Spectral Decomposition of a Symmetric Linear Operator on a subset S on a Euclidean Space V, Positive Definite Operators and their Square Roots, Polar Decomposition Theorem, and the Representation Thm for orthogonal Operators.  It mathematically presents tensors over a Euclidean Space, presents traditional continuum mechanics (again, no thermodynamics), and gives exercises.  Not much in the way of physical motivation.

 

5.      GOBAG Informal Write-ups in Mechanics.  A web page kept updated by R. Brannon.
        It contains miscellaneous notes/tutorials collected from a variety of people on particular topics.  Of special interest to our class is her writeup on Elementary vector and tensor analysis for Engineers (pdf file, 122 pp, and more advanced than what we will cover here), and her writeup on curvilinear coordinates, the first part of which would make a good project topic.

 

6.      Chadwick, P.,  Continuum Mechanics, Concise Theory and Problems, New York, Dover, originally published in 1976.  (not expensive).
        This is a small book, similar to Kennett, above, but is more mathematical in the presentation of tensors and does not give as much physical motivation.  Again, no indicial notation and no thermodynamics.

 

7.      Heinbockel, John H.    Introduction to Tensor Calculus and Continuum Mechanics.   A web page.
         This book has two parts, the first part is equivalent to a semester long course on tensor calculus (especially coordinate transformation, covariant and contravariant coordinates), and the second part is an introduction to continuum mechanics (no thermodynamics) in which all equations are presented in generalized coordinates.

 

8.      Malvern, Lawrence E. Introduction to the Mechanics of a Continuous Medium, 1969, Prentice-Hall.  This use to be the textbook for this course but it is now, unfortunately, out of print.  It gives a very thorough explanation of engineering terms for both a fluid and a solid and is a very nice reference.

 

9.      Fung, Y. C. A First Course in Continuum Mechanics, 1994, Prentice Hall, ISBN 0-13-061524-2.  This text book motivates the material using biological examples and is easy to understand.  Especially recommended for understanding terms in solid mechanics.

 

Important Dates and Information

Note that all CLAS students must always have an accurate mailing and e-mail address:  http://www.cudenver.edu/registrar and students are responsible for completing financial arrangements with financial aid, family, scholarships, etc.

Spring 2008 Important Dates


  • January 27, 2008; Last day to be added to a wait list
  • January 22 – February 6, 2008; Students are responsible for verifying an accurate spring 2008 course schedule via the SMART registration system.  Students are NOT notified of their wait-list status by the university.  All students must check their schedule prior to February 6, 2008 for accuracy.
  • January 28, 2008 at 5PM; Wait lists are dropped.  Any student who was not added to a course automatically from the wait list by this date and time MUST complete a drop/add form to be added to the class.  Students are NOT automatically added to the class from the wait list after this date and time.
  • January 29, 2008; First day an instructor may approve a request to add a student to a course using the Schedule Adjustment Form (drop/add form).
  • January 27, 2008; Last day to add a course using the SMART Web Registration system. Students MUST check their registration to verify what classes they are enrolled in.
  • February 6, 2008 at 5 PM; Last day to add structured courses without a written petition for a late add.  This is an absolute deadline and is treated as such. This deadline does not apply to independent study, internships, and late-starting modular courses.
  • February 6, 2008 at 5 PM; Last day to drop a spring 2008 course with a full tuition refund and no transcript notation.  Drops after this date will appear on your transcript.  This is an absolute deadline and is treated as such.
  • February 6, 2008 at 5 PM; Last day to completely withdraw from all spring 2007 courses with a full tuition refund and no transcript notation.  Drops after this date will appear on your transcript.  This is an absolute deadline and is treated as such.
  • February 6, 2008 at 5 PM; Last day for students to apply for spring 2008 Graduation.  Students MUST see their CLAS advisor to obtain a Graduation Application.
  • February 6, 2008 at 5 PM; Last day to request pass/fail option for a course.
  • February 6, 2008 at 5 PM: Last day to request a no credit option for a course.
  • February 6, 2008 at 5 PM: Last day to register as a Candidate for Degree.
  • February 6, 2008 at 5 PM: Last day to petition for a reduction in thesis or dissertation hours.
  • April 7, 2008 at 5 PM; Last day for Non-CLAS students to drop individual classes or withdraw from all classes without a petition and special approval from the student’s academic Dean. This is treated as an absolute deadline.
  • April 18, 2008 at 5 PM; Last day for CLAS students to drop individual classes or withdraw from all classes without a petition and special approval from the student’s academic Dean. This is treated as an absolute deadline.
  • No schedule changes will be granted once finals week has started.  There are NO exceptions to this policy.

 

Consult the Academic Calendar for details on registration/payment deadlines:  http://www.cudenver.edu/registrar  

 

Incomplete grades: Incomplete grades (IW or IF) are NOT granted for low academic performance.  To be eligible for an incomplete grade, students MUST

1.     Successfully complete a minimum of 75% of the course,  

2.      Have special circumstances beyond their control that preclude them from attending class and completing graded assignments, and

3.       Make arrangements to complete missing assignments with the original instructor via completion of a CLAS Course Completion Agreement.  Verification of special circumstances is required.

The CLAS Course Completion Agreement is available from the CLAS Advising Office, NC 2024 or from the Department of Mathematics.