Elasticity/More variational principles

More variational principles edit

Recall that the admissible states appropriate to the minimum principles are required to meet certain field equations and the appropriate boundary conditions.

In some cases, we would like to use variational principles in which the admissible states satisfy as few constraints as possible. Such variational principles are useful for symmetric elastic fields.

Let   be a scalar-valued functional. Let   be the set of all admissible states.

Let   and   be two admissible states  . Let   be a Lagrange multiplier such that   is also an admissible state  .





only if   exists and equals zero for all   that satisfy the above requirements.

There is an infinite number of possible functional   that satisfy these requirements. Two examples are:

  • The Hellinger-Reissner functional
  • The Hu-Washizu functional