BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Engineering - Mechanics and Materials Seminar Seri
es
SUMMARY:Counting with symmetry for structural mechanics -
Dr Simon Guest\, CUED
DTSTART;TZID=Europe/London:20151120T140000
DTEND;TZID=Europe/London:20151120T150000
UID:TALK61011AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61011
DESCRIPTION:Counting components\, and then comparing the numbe
r of constraints with number of degrees of freedom
available to a structure\, is a good first step i
n evaluating likely structural behaviour. Maxwell
first described this in 1864 when he stated that\
, in general\, a structure with j joints would req
uire 3j-6 bars to make it rigid. Later Calladine
generalised this idea by pointing out that the dif
ference between the number of bars and 3j-6 counts
the difference between the number of mechanisms a
nd the number of states of self-stress. Sometimes\
, just simple counting can lead to profound insigh
ts\, such as showing that any stiff repetitive str
ucture must necessarily be overconstrained.\n\nThi
s talk will introduce the idea that any rule that
involves counting components can be expanded to a
more general symmetry version that involves counti
ng the symmetries of sets of components\, and that
this counting can practically be done by simply c
onsidering the number of components that are unshi
fted by particular symmetry operations. This prov
ides useful insight into why certain symmetric str
uctures are able to move despite apparently having
enough members to make them rigid\, or that tense
ngrity structures can be rigid without having 'eno
ugh' members.\n\nThe talk will describe a recent r
esult on 'auxetic' materials: a symmetry criterion
that shows when a periodic system made up of bars
\, bodies and joints has an 'equiauxetic' mechanis
m\, that is\, show the limiting behaviour of Poiss
on ratio equal to -1\, with equal expansion/contra
ction in all directions. Such systems can provide
good models for the design of lattice materials wi
th high\, stretching-dominated\, shear modulus\, b
ut low\, bending-dominated\, bulk modulus.
LOCATION:Department of Engineering - LT2
CONTACT:Ms Helen Gardner
END:VEVENT
END:VCALENDAR