On concentrated loads and green's functions in elastostatics

Abstract

This investigation is concerned with the notion of concentrated loads in classical elastostati cs and related issues. Following a li1nit treatment of problems involving concentrated internal and surface loads, the orders of the ensuing displacements and str e ss singularities, as well as the stress resultants of th e latter , are dete rmined. These conclusions are taken as a basis for an alternative direct formulation of concentrated-load problems, the completeness of which is established through an appropriate uniqueness theor em. In addition, the pr esent work supplies a r ecipr ocal theorem and an integral representation-theorem applicable to singular problems of the type unde r consideration. Finally, in the course of the analysis presented here, the theory of Green's functions in elastostatics is extended .

Integral representations in elastostatics and their application to an alternative boundary element method

“…Turteltaub and Sternberg [1]). The relation is viewed as an integral equation system which is solved numerically.…”

“…If we set p = 1 and v = e 1 (i.e. v = 1), then (38) provides u , 1 . Similarly, if we set p = 1 and v = e 2 (i.e.…”

“…Whenever stresses at infinity are specified, the solution [u, ] to the original problem may be viewed as the sum of the solutions to two auxiliary problems. To this end, we decompose the displacement and stress fields as u = u (1) + u (2) and = (1) + (2) where [u (1) , (1) ] and [u (2) , (2) ] are the solutions to the auxiliary problems. The fields associated with [u (1) , (1) ] are u (1)…”

“…We prescribe the boundary conditions for the second auxiliary problem from the fact that (2) n = n − (1) n and u (2) = u − u (1) . In particular, for the case considered in this section, the stresses at infinity must be zero and the traction on the elliptical boundary must be equal to − ∞ n .…”

A New Mathematical Foundation for Contact Interactions in Continuum Physics

“…In a series of papers, Marzocchi & Musesti have refined the results of [15] where the decomposition of general interactions into a body and a contact part (in analogy to [26,28]) and corresponding structural properties are investigated in [31], thermodynamical aspects are treated in [32], a more general class of bodies is studied in [34], and the treatment of boundary conditions is considered in [35]. For the investigation of concentrated forces in the framework of linear elasticity we refer to the papers of Boussinesq [6] [61], and references therein.…”