Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published July 1981 | public
Journal Article

The effect of nonlinearity on a principle of Saint-Venant type


This paper establishes a principle of Saint-Venant type associated with finite anti-plane shear of a cylinder whose cross-section is a semi-infinite strip. The long sides of the strip are traction-free, and the short side carries an arbitrarily distributed shear traction. At the infinity in the strip, the deformation is prescribed to be one of simple shear, and the associated shear stress is uniform. The analysis is based on the fully nonlinear theory of finite elastostatics and is carried out for a special class of homogenous, isotropic incompressible materials. It is shown that, along the parallel sides of the strip, the nonvanishing component of shear stress differs from its average value (taken across the strip) by an exponentially decaying function of the distance from the end. A lower bound is given for the rate of decay.

Additional Information

© 1981 Sijthoff & Noordhoff International Publishers. Received December 17, 1979. We are grateful to Eli Sternberg for reading the manuscript and ma king a number of helpful suggestions. One of the authors (C.O.H.) acknowledges the support of the National Science Foundation under Grant ENG 78-26071. The work was completed during August 1979, while this author held an appointment as Visiting Associate in Applied Mechanics, Division of Engineering and Applied Science, California Institute of Technology.

Additional details

August 19, 2023
October 18, 2023