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SUMMARY:Counting with symmetry for structural mechanics - Dr Simon Guest\,
  CUED
DTSTART:20151120T140000Z
DTEND:20151120T150000Z
UID:TALK61011@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:Counting components\, and then comparing the number of constra
 ints with number of degrees of freedom available to a structure\, is a goo
 d first step in evaluating likely structural behaviour.  Maxwell first des
 cribed this in 1864 when he stated that\, in general\, a structure with j 
 joints would require 3j-6 bars to make it rigid.  Later Calladine generali
 sed this idea by pointing out that the difference between the number of ba
 rs and 3j-6 counts the difference between the number of mechanisms and the
  number of states of self-stress. Sometimes\, just simple counting can lea
 d to profound insights\, such as showing that any stiff repetitive structu
 re must necessarily be overconstrained.\n\nThis talk will introduce the id
 ea that any rule that involves counting components can be expanded to a mo
 re general symmetry version that involves counting the symmetries of sets 
 of components\, and that this counting can practically be done by simply c
 onsidering the number of components that are unshifted by particular symme
 try operations.  This provides useful insight into why certain symmetric s
 tructures are able to move despite apparently having enough members to mak
 e them rigid\, or that tensengrity structures can be rigid without having 
 'enough' members.\n\nThe talk will describe a recent result on 'auxetic' m
 aterials: a symmetry criterion that shows when a periodic system made up o
 f bars\, bodies and joints has an 'equiauxetic' mechanism\, that is\, show
  the limiting behaviour of Poisson ratio equal to -1\, with equal expansio
 n/contraction in all directions. Such systems can provide good models for 
 the design of lattice materials with high\, stretching-dominated\, shear m
 odulus\, but low\, bending-dominated\, bulk modulus.
LOCATION:Department of Engineering - LT2
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