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Extension And Application Of The Sedov-Berdichevskii Variational Principle, Francis X. Prendergast

Dissertations

The Sedov-Berdichevskii variational principle is extended, and this extended principle is employed in the construction of a shell theory.

The extension of the principle is accomplished by the use of Lagrangian multipliers, and a redefinition of terms in order to maintain the original generality of the principle. The Euler equations of the extended variational principle provide, in addition to those obtained in the original principle, elastic and plastic kinematic relations, and, elastic and plastic constitutive relations. Also, the Euler equations of the original principle are obtained in a physically more meaningful form. Examples are given which show how this principle …