The effect of constitutive law perturbations on finite antiplane shear deformations of a semi-infinite strip

Authors:
C. O. Horgan and L. E. Payne

Journal:
Quart. Appl. Math. **51** (1993), 441-465

MSC:
Primary 73C10; Secondary 73B99, 73C50, 73G05

DOI:
https://doi.org/10.1090/qam/1233524

MathSciNet review:
MR1233524

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Abstract: This paper is concerned with assessing the effects of small perturbations in the constitutive laws on antiplane shear deformation fields arising in the theory of nonlinear elasticity. The mathematical problem is governed by a second-order quasilinear partial differential equation in divergence form. Dirichlet (or Neumann) boundary-value problems on a semi-infinite strip, with nonzero data on one end only, are considered. Such problems arise in investigation of Saint-Venant end effects in elasticity theory. The main result provides a comparison between two solutions, one of which is a solution to a simpler equation, for example Laplace's equation. Three examples involving perturbations of power-law material models are used to illustrate the results.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1233524

Article copyright:
© Copyright 1993
American Mathematical Society