THE EFFECT OF CONSTITUTIVE LAW PERTURBATIONS ON FINITE ANTIPLANE SHEAR DEFORMATIONS OF A SEMIINFINITE STRIP

This paper is concerned with assessing the effects of small perturbati ons in the constitutive laws on antiplane shear deformation fields ari sing in the theory of nonlinear elasticity. The mathematical problem i s 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 conside red. Such problems arise in investigation of Saint-Venant end effects in elasticity theory. The main result provides a comparison between tw o solutions, one of which is a solution to a simpler equation, for exa mple Laplace's equation. Three examples involving perturbations of pow er-law material models are used to illustrate the results.