Work-Conjugate Boundary Conditions in the Nonlinear Theory of Thin Shells

Abstract

Work–conjugate boundary conditions for a class of nonlinear theories of thin shells formulated in terms of displacements of the reference surface are discussed. Applying theorems of the theory of differential forms it is shown that many of the sets of static boundary conditions which have been proposed in the literature do not possess work–conjugate geometric counterparts. The general form of four geometric boundary conditions and their work–conjugate static boundary conditions is constructed and three particular cases are analyzed. The boundary conditions given here are valid for unrestricted displacements, rotations, strains and/or changes of curvatures of the reference surface.