Two Problems in Plane Finite Elastostatics

Author: Connolly, Jeremiah Finbarr

Year: 1983

Degree: Dissertation (Ph.D.)

Advisor: Knowles, James K.

Committee Members: Sternberg, Eli; Cohen, Donald S.; Knauss, Wolfgang Gustav; Knowles, James K.; Miklowitz, Julius

Option: Applied Mechanics

DOI: 10.7907/yhjy-mb48

Abstract

In this paper the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids is used to study the elastostatic fields in plane strain near the point of application of a concentrated force on a deformed half plane and near the vertex of a circular sector whose plane deformed faces are subjected to prescribed tractions.

In the concentrated force problem, restricting only the form of the elastic potential at large extensional deformations, it is shown that, for materials which "harden" in simple shear, the displacement is bounded at the point of application of the load. This is not the case for materials which "soften" in shear. Estimates of the true stress tensor near the singular point are given.

In the sector problem, for a class of the materials mentioned, the deformation and stress field near the vertex of the deformed cross-section are derived and discussed.

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