UPDATED: 9/23/99

Roger F. Gans  my home page a student's eye view office: Hopeman 330  phone: 5-2123  e-mail: gans@me.rochester.edu

CLASSES: TR 1525-1640, Gavett 208

OFFICE HOURS: TR before class (1400-1515) and R after class (T if it's a short meeting), W 1400-1600, or by appointment. (I'm typically in before 0800 and meeting me first thing in the morning is certainly possible.)

THE COURSE: The course covers plates and shells with an emphasis on shells (an outline below).  Both are essentially two-dimensional objects: plates are flat and shells are curved.  There's a nice architectural web site maintained by the University of Virginia on which you can find some architectural shells.    (This is where the illustration at the top of the page comes from.)   Take a look at some of nature's shells as well.  We will explore the approximations to elasticity theory that allow us to calculate the behavior of plates and shells, although we will avoid formal asymptotic analysis.  We will be limited to linearly elastic materials with small strains and small deformations, and we will work with steady-state behavior only.  You will need to have some memory of your strength of materials course(s) and a solid feel for vectors.  It is impossible to deal with elasticity without some use of tensors, but we will avoid any serious exploration of tensors, treating them as three by three arrays with physical meaning.

TEXTS

Gould, P. L. Analysis of Plates and Shells Prentice Hall: Upper Saddle River, NJ  1999
 

GRADING

Homework: due most Thursdays in class [late homeworks will not be accepted] (30%)

There will be 10-12 problem sets, of which I will throw out the lowest grade. It is OK to work together on the homework sets, but I want individual work handed in, and I expect every member of a study group to contribute to the effort. Be careful about this; it is easy to think you are contributing when you are not.

Exams:

midterm exam: (date TBA, probably take-home, individual work required). (30%)

final exam:  (40%)

Both exams will be open book-open notes

The following outline is subject to change as we go along. I will be updating the schedule on a weekly basis.
 

1. Introduction: What are plates and shells? The fundamental two dimensional hypothesis. The nature of approximation(s).  Review of linear elasticity.  Beam theory as exemplar.

2. Elementary asymptotics:  What it means to be thin.  Kirchhoff's hypothesis.  Plate equations.

3. Some example of plate deformation:

4. Geometry:  Curves and surfaces.  Tangent, normal and binormal vectors, curvature and torsion.  Mean and Gaussian surface curvatures.  Surface and normal vectors.

5. Cylindrical shells:

6. Axisymmetric shells:

7. General three dimensional shells:

8. Finite element analysis (??): we won't actually do this, but we ought to have some sort of introduction to this topic and set of techniques.

I have put a number of books and papers on reserve in Carlson.  Check this from time to time as I hope to update this as we go along, and as we discover useful references in the literature.  Feel free to go to the library on your own.  If you find something really neat, mail it to me.