Page 129 - Introduction to Continuum Mechanics
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114 Kinematics of a Continuum
from which we obtain
3.16 Compatibility Conditions for Infinitesimal Strain Components
When any three displacement functions MI, u^, and u$ are given, one can always determine
dUj
the six strain components in any region where the partial derivatives -r^r exist. On the other
oJLs
are
hand, when the six strain components (^11^22^33^12^13^23) arbitrarily prescribed in
M
some region, in general, there may not exist three displacement functions (#i,«2» 3)> satisfying
the six equations
For example, if we let
du-i i du?
then, from Eq. (3.16.1) —• = X 2 and from Eq. (3.16.2), ~~ = 0, so that
OAj 0A2
