On the derivation of boundary conditions for plate theory

Abstract

Previous work on the derivation of plate theory by parametric expansions in three-dim ensional elasticity includes expansion of the interior solution (Goodier 1938) and simultaneous expansions of interior and edge-zone solutions (Friedrichs 1950; Friedrichs & Dressier 1961). The work of Goodier is concerned with the derivation of two-dim ensional differential equations while the work of Friedrichs & Dressier is concerned with the derivation of differential equations as well as boundary conditions, through the joint consideration of interior and edge-zone expansions. The principal object of the present paper is the derivation of boundary conditions for the successive terms of the interior solution expansion, without consideration of the edge-zone solution expansion. The method of derivation makes use of a variational formulation of three-dimensional elasticity theory.