On the application of a Baecklund transformation to linear isotropic elasticity

Abstract

Baecklund transformations have been employed in gas-dynamics to reduce the hodograph equations to appropriate canonical forms in subsonic, transonic and supersonic flows; thus, for example, the important Kàrmàn-Tsien approximation may be generated as a consequence of a simple Baecklund transformation of the hodograph system. Here, it is shown that Weinstein's correspondence principle in generalized axially symmetric potential theory emerges as a particular member of a class of Baecklund transformations of the Stokes-Beltrami equations. An iterated form of the correspondence principle may be used to obtain solutions to certain boundary-value problems involving axiallysymmetric deformations of an incompressible isotropic linear elastic material. Such solutions assume an added importance in the light of recent work by Selvadurai & Spencer, where the first order theory serves as the basis for solutions in second order incompressible finite elasticity. © 1974 by Academic Press Inc. (London) Limited.