Non‐linear boundary value problems for the annular membrane: New results on existence of positive solutions

The Foppl-Hencky theory of small finite deflections has been applied to the study of axisymmetric deformations of annular membranes by various authors. The mathematical problem of uniqueness of tensile solutions for the corresponding non-linear boundary value problems in the full range of physically meaningful boundary data was solved only recently.3, 4 In this paper, a new integral equation technique of solution is developed which yields the existence of tensile solutions for a parameter range of the boundary data where previous investigations on this matter had not been successful. It is shown that tensile solutions no longer exist, when sufficiently large positive radial displacements are prescribed at the inner edge of the annulus.