On the Somigliana dislocations associated with applications of the Neuber–Papkovich solution in multiply-connected regions

Summary The study aims to explain the problem of single-valuedness of the mean stress and dilatation in multiply-connected regions. It is shown that in multiply-connected regions, displacement representation potentials, in particular the Neuber–Papkovich potentials, have to be submitted to the integral conditions in order to avoid the many-valuedness. Received 8 September 1998; accepted for publication 8 April 1999