Variational Principles in Nonlinear Continuum Mechanics

摘要

The paper deals with general variational principles for a wide class of nonlinear problems in continuum mechanics and thermodynamics. By a variational principle is meant a theorem concerning stationary values of a well-defined functional, as distinct from Galerkin integrals or 'virtual work' principles associated with a given physical law. The essential features of a general theory of potential operators on Banach spaces and the field equations governing the thermodynamics of continua are first reviewed. Then a functional K(lambda) is generated which assumes a stationary value when the entire collection of field equations governing the behavior of the continuum are satisfied. (Author)