Eli Sternberg

Theorems in linear elastostatics for exterior domains

Abstract : Conventional proofs of fundamental theorems in three-dimensional classical elastostatics such as the traditional proofs of the uniqueness and reciprocal theorems or of the minimum e ergy principles are generaliz d to unbounded domains exterior to a finite number of closed surfaces.

ON THE ANALYSIS OF THERMAL STRESSES IN VISCOELASTIC SOLIDS

Abstract : This paper is devoted exclusively to solids that, under isothermal conditions and for infinitesimal strains, exhibit linear viscoelastic behavior. An attempt is made to sketch a systematic account of relevant recent theoretical developments; it is attempted to supply a helpful, if necessarily incomplete, guide to available specific results and to the literature on the subject at hand. The present treatment is largely confined to the quasi-static analysis of thermal stresses in homogeneous and isotropic, linear viscoelastic media. Questions regarding inhomogeneous and anisotropic solids, inertia effects, and thermo-mechanical coupling effects are touched upon.

Note on the expansion in powers of Poisson's ratio of solutions in elastostatics

In this paper we examine the power-series development with respect to Poissons ratio of the solution to the second boundary-value problem (surface tractions prescribed) in three-dimensional classical elastostatics for the case of vanishing body forces. The individual terms of this expansion, by means of steady-state thermoelasticity theory, are found to admit an independent physical interpretation. This interpretation, in turn, permits certain conclusions concerning the dependence upon the elastic constants of solutions to space problems. In particular, it is shown that for a body of arbitrary connectivity all stresses are independent of the elastic constants if and only if the dilatation (and the mean normal stress) is a linear function of the cartesian coordinates. The feasibility of successive approximations of solutions appropriate to sufficiently small values of Poissons ratio is also considered.

Steady-state thermal stresses in an elastic cone

ZusammenfassungDiese Arbeit befasst sich mit der Bestimmung der stationären Wärmespannungen, die in einem elastischen Kreiskegel durch eine unstetige Verteilung der Oberflächentemperatur hervorgerufen werden. Die Temperatur der Mantelfläche wird oberhalb und unterhalb einer festen Entfernung von der Kegelspitze konstant angenommen. Das zugehörige Wärmeleitungsproblem wurde in einer früheren Veröffentlichung unabhängig gelöst. In der vorliegenden Arbeit wird eine strenge Lösung für die gesuchten Wärmespannungen mit Hilfe der Mellin-Transformation hergeleitet. Das hier benutzte Verfahren ist auch anwendbar auf das gewöhnliche Randwertproblem für einen elastischen Kegel, der durch eine entsprechende unstetige Oberflächenbelastung beansprucht wird.