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 William O. Williams
Professor
Ph.D., Brown University
Office: Wean Hall 6202
Phone: (412) 268-6400
E-mail: wow@cmu.edu
Research
My research generally concerns the formulation and analysis of models in mechanics and
thermodynamics.
Most recently I have been involved in studies in mechanics whose
central point is that of the effect of constraints. At the extreme
point are systems which have no internal energy at all, and hence have
internal forces which are purely reactions to constraints. A
historical example is that of Tchebychev Nets, which were developed by
Tchebychev, Servant and Voss in the last century as models for the
deformation of cloth. In an older article listed below, I examined the
stresses and concentrated forces possible in such systems. More
recently, I have become interested in Tensegrity Structures, whose
internal forces likewise are purely constraint-generated. These
structural trusses, whose elements consist of both rigid bars and
cables, were originated by Snelson and developed by Buckminster Fuller,
and present interesting technical and mathematical problems. Both of
these systems can be treated by relaxation from elastic or partially
elastic models,
In work with Podio Guidugli and diCarlo I have considered the
approach of treating shells as examples of constrained
three-dimensional bodies. This point of view leads in a natural way
to two-dimensional models with various degrees of microstructure.
I also have a on-going interest in mathematical models in
physiology. In an older work I advanced a model for contraction of
muscle fibers that can represent most observed micro-experimental
responses in muscle fibers; a goal is to extend this to whole-muscle
models. Currently I am investigating applications of the
above-mentioned constrained systems to biological models.
Selected Publications
W. Williams, (2011) "Huxley's Model of Muscle Contraction with Compliance", J. Elasticity,
to appear.
Preprint
A. Micheletti and W. Williams, (2007) "An Evolutionary Procedure for Form-finding for
Tensegrity Structures ", J. Mech. of Materials
and Structures, 2:857--882, 2007.
Preprint
W. Williams, (2003) "A Primer on the Mechanics of Tensegrity Structures ", to appear.
Preprint
Oppenheim, O. J. and W. O. Williams, (2001), "Vibration of an Elastic Tensegrity Structure," Eur. J. Mech. A, 20:1023--1031.
Preprint
A.
diCarlo, P. Podio Guidugli and W. Williams (2000), "Shells with
Thickness Distension", Int. J. Solid. Struct., 38:7405-7429.Preprint
Oppenheim, O. J. and W. O. Williams, (2000), "Geometric effects in an elastic tensegrity structure," J. Elasticity, 59:51-65.
Preprint
W.
Williams, (1991), "Forces in Tchebechev nets ", in Waves and Stability
in Continuous Media, ed. S. Rionero, World Scientific, New Jersey,
408-418.
W. Williams. (1990), "A Purely Mechanical Model of Muscular Contraction,"
Math. Biosc. 100: 249-278.
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