On non-classical boundary conditions

Abstract

To determine the deformation of a body from the system of differential equations governing its thermo-mechanical deformations, we need side conditions such as boundary conditions. The most frequently employed boundary conditions are those of place and/or traction in a purely mechanical problem and of temperature and/or heat flux in a thermal problem. These and other more familiar mechanical boundary conditions are summarized by SEWELL [1, eqns. (9)-(13)]. The frequently considered thermal boundary conditions are discussed by CARSLA W & JAEGER [2, Chapter 1]. It seems that the interest in non-classical mechanical boundary conditions originated in the study of elastic stability, and a convenient reference for the various mechanical loadings considered up to 1961 is the book by BOLOTIN [3]. In this book, nOLOTIN discusses many elastic-stability problems under follower loads, defined as those which follow in a prescribed manner the deformation of the surface element upon which they are acting. More general than these are the configuration-dependent loadings [1] defined * by an a priori assumption that the load