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SUMMARY:Counting with symmetry for structural analysis - Dr Simon Guest\, 
 CUED
DTSTART:20151120T140000Z
DTEND:20151120T150000Z
UID:TALK61016@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 desc
 ribed this in 1864 when he stated that\, in general\, a structure with j j
 oints would require 3j-6 bars to make it rigid. Later Calladine generalise
 d this idea by pointing out that the difference between the number of bars
  and 3j-6 counts the difference between the number of mechanisms and the n
 umber of states of self-stress. Sometimes\, just simple counting can lead 
 to profound insights\, such as showing that any stiff repetitive structure
  must necessarily be overconstrained.\n\nThis talk will introduce the idea
  that any rule that involves counting components can be expanded to a more
  general symmetry version that involves counting the symmetries of sets of
  components\, and that this counting can practically be done by simply con
 sidering the number of components that are unshifted by particular symmetr
 y operations. This provides useful insight into why certain symmetric stru
 ctures are able to move despite apparently having enough members to make t
 hem rigid\, or that tensengrity structures can be rigid without having ‘
 enough’ members.\n\nThe talk will describe a recent result on ‘auxetic
 ’ materials: a symmetry criterion that shows when a periodic system made
  up of bars\, bodies and joints has an ‘equiauxetic’ mechanism\, that 
 is\, show the limiting behaviour of Poisson ratio equal to -1\, with equal
  expansion/contraction in all directions. Such systems can provide good mo
 dels for the design of lattice materials with high\, stretching-dominated\
 , shear modulus\, but low\, bending-dominated\, bulk modulus.
LOCATION:Department of Engineering - LR2
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