Wrinkle-free solutions of circular membrane problems
The paper is devoted to the study of rotationally symmetric deformation of a plane circular membrane subjected to an axial surface load. On the edge of the membrane either radial stresses or radial displacements are prescribed. The investigation is based on the Reissner's geometrically nonlinear theory for thin membrane without restrictions on the magnitude of displacements and rotations. At present, there are no general results available for arbitrarily loaded circular membranes with traction-free edges. This paper fills this gap. In the paper the set of all radial displacements associated with traction-free edge has been obtained. The range of the boundary parameters has been decomposed into complementary domains of existence and nonexistence of tensile solutions, i.e. solutions that are governed by a nonnegative radial stress components. The separatrix which forms the common boundary has been discussed both analytically and numerically. The authors have obtained a restricted set of those solutions for which the principal stresses are nonnegative. Natural boundary of a wrinkle-free solution has been determined for the cases when radial stresses or radial displacements are prescribed on the membrane edge.
scientific article; zbMATH DE number 63812
scientific article