Math 499: Michell Truss PFUG
Course Description:
Anthony George Maldon Michell was a mechanical engineer in the early part of the last century, who formulated the following variational problem from mechanics; what configuration of bars and cables needed to withstand a system of equilibrated point forces is most economical? By "economical" we are to understand that the cost of a bar or beam is proportional to its length and strength. Michelle constructed several interesting examples of trusses that are most economical by means of calibration vector fields. Consider the following example; Suppose three point forces lie on the vertices of an equilateral triangle and parallel to their position away from the origin. There are several ways to build a truss that withstands these point forces. Here are a few.

By means of the calibration vector field &phi(x) = x, one can show that the first two have the same cost while the third necessarily costs more because it uses both cables and bars The problem is interesting, because although the set of trusses which withstand a given system of point forces is convex subset of the (infinite dimensional) space of trusses and the cost function is convex, the set of admissable perturbations of a truss is virtually indescribable. This PFUG will examine Michell's examples, why the above claim is true and construct criterion for a truss to be economical. Open questions surrounding the Michell truss problem are Participants in this PFUG are encouraged to have some knowledge of vector calculus, elementary differential geometry and linear algebra.
Meeting Time: W 4:00-4:50, Tr 12:10-1:00, F 5:00-5:50
Location: 117 HZ, Weiss, 453 HB

Instructor:
Rolf J. Ryham
Email: [my last name] at rice dot edu
Phone: x2385
Office: Herman Brown 452

References:
Michell Trusses and Lines of Principal Actions. (G. Bouchitte, W. Gangbo, P. Seppecher), Math. Models Meth. Applied Sci., 2008.

Disabilities Statement:
Any student with a documented disability needing academic adjustments or accommodations should speak to me as soon as possible, preferably during the first two weeks of class. I will be happy to help you, and all communications will remain confidential. As a reminder, you will also need to contact Disability Support Services in the Ley Student Center (www.dss.rice.edu). If you believe that you have an undocumented disability, you are encouraged to talk to me and Disability Support Services so that you can get help.