Variational Principles of the Variable Boundary for the Elastoplastic Body

The variation problem of an elastoplastic body is considered as the variation problem of variable boundary.If the first variation vanishes, the mathematical physical equation satisfying the unknown function can be derived with calculus of variation for variable boundary and variational principles of variable boundary for an elastoplastic body can also be established which completely described the elastoplastic problem. These priciples comprise successive equation of elastic and plastic domains, the physical equation is satisfied by the stress and strain along the stress(strain) pass and the subsidiary boundary condition on the whole boundary of the given surface forces. If the influence of the variable boundary is neglected, this kind of variational principles is degenerated to the common variational principles.