© 1997 by Oxford University Press
ON THE SOLUTIONS OF BOUSSINESQ, LOVE, AND REISSNER AND WENNAGEL FOR AXISYMMETRIC ELASTIC DEFORMATIONS
( 4 Langville Court, East Malvern, 3145 Melbourne, Australia )
The completeness of Boussinesq's and Love's axisymmetric stress functions are examined without excluding the axis of axisymmetry. Contrasting properties are found for the apparently similar functions of Boussinesq and Love. The former is complete if either the body of revolution is simply connected or the meridional half-section of the body is simply connected (hence the body may contain internal voids), the latter if either the full meridional section is simply connected or the axis of symmetry does not intersect the body whose meridional half-section is simply connected (hence the body cannot have any internal void). Boussinesq's solution can also be extended to multiply-connected regions with the augmentation by the curl of a solenoidal axisymmetric vector field. The associated problem of axisymmetric pure torsion is also examined using the same technique. Its displacements are found to becompletely expressible in terms of one harmonic function if either the meridional full section is simply connected or the axis of symmetry does not intersect the body whose meridional half-section is simply connected. The completeness of the Reissner and Wennagel solution and the differentiability to any order of its displacement function are derivable from this consideration.