The stress functions then obey a single differential equation which corresponds to the compatibility equations.
2.
This relation is equivalent to the set of strain-compatibility equations as well as of the displacement boundary conditions on the part S _ u.
3.
The solution to the elastostatic problem now consists of finding the three stress functions which give a stress tensor which obeys the Beltrami-Michell compatibility equations.
4.
The constraints on the strain tensor that are required to assure that this is the case were discovered by Saint Venant, and are called the " Saint Venant compatibility equations ".
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