The Governing Equations and Extremum Principles of Elasticity and Plasticity Generated from a Single Functional*—Part I

Abstract

A new theoretical framework is described which generates, in a characteristic or canonical form, the governing equations and (if appropriate) inequalities of a wide class of problems in applied mathematics from a single generating functional. Variational and dual extremum principles are expressed in terms of that functional. The theory is first illustrated, here in Part I, by applying it to the familiar contexts of classical elasticity and the rigid/plastic yield-point problem. Precise identification of certain linear operators and inner product spaces is entailed. The unifying effect of the theory is emphasized by working out, in a sub-sequent Part II, further applications in finite elasticity and in incremental plasticity from a stressed state with allowance for geometry changes. New results are obtained, and the connection indicated between certain approximate methods of structural mechanics, in particular the finite-element method.