On the derivation of well posed boundary value problems in structural mechanics. : Kerr, AD Princeton Univ., New Jersey, USA 5F,18R Int. J. Solids, Struct. V12, N1, 1976, P1–11

Abstract

Abstract The paper starts with a discussion of a number of published boundary value problems in structural mechanics, whose intuitive formulation led to incorrect boundary or matching conditions. It is then shown on three examples, using variational methods, how to obtain well posed formulations for problems of this type. For uniformity of presentation, all examples deal with continuously supported beams. The first two examples exhibit boundary and matching points whose position is fixed along the beam axis. In the third example it is shown how to use the method of variational calculus for a variable end point to formulate structural problems with variable matching points. This is demonstrated on the problem of a beam which rests on, but is not attached to, a Pasternak base; thus where parts of the beam may lift off the base. Each example concludes with a comparison and discussion of related formulations published in the literature.