Compatibility Equation
93 If £ij = 1 (ui,j + uj,i) then we have six differential equations (in 3D the strain tensor has a total of 9 terms, but due to symmetry, there are 6 independent ones) for determining (upon integration) three unknowns displacements ui. Hence the system is overdetermined, and there must be some linear relations between the strains.
94 It can be shown (through appropriate successive differentiation of the strain expression) that the compatibility relation for strain reduces to:
There are 81 equations in all, but only six are distinct d2£11 , d2£22
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Ashley Scott8 years ago
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