Introduction to Elasticity/More variational principles

From Wikiversity
Jump to navigation Jump to search

More variational principles[edit | edit source]

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 .


Let

Then,

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