Elasticity/Hellinger-Reissner principle
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Hellinger-Prange-Reissner Variational Principle[edit | edit source]
In this case, we assume that the elasticity field is invertible and is smooth on . We also assume that is the set of all admissible states that satisfy the strain-displacement relations, the traction-stress relations and the balance of angular momentum.
Let denote the set of all admissible states and let be a functional on defined by
for every .
Then,
at an admissible state if and only if is a solution of the mixed problem.