Wrinkle-free solutions of circular membrane problems
type: Item
instance of: scholarly article
title: Wrinkle-free solutions of circular membrane problems
zbMATH Open document ID: 0782.73035
DOI: 10.1007/BF00946242
author: Armin Beck
author: Hans Grabmüller
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1992-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 63812
zbMATH Keywords: Reissner theory
zbMATH Keywords: rotational symmetric deformation
zbMATH Keywords: radial stresses
zbMATH Keywords: radial displacements
zbMATH Keywords: traction-free edge
zbMATH Keywords: tensile solutions
zbMATH Keywords: separatrix
MaRDI profile type: Publication
cites work: Non-linear boundary values problems for the circular membrane
cites work: Membrane buckling: A study of solution multiplicity
cites work: The plane circular elastic surface under normal pressure
cites work: Q3286428
cites work: Positive Solutions of Annular Elastic Membrane Problems with Finite Rotations
cites work: Wrinkle-free solutions in the theory of annular elastic membranes
cites work: Finite displacements of annular elastic membranes
cites work: Q3876150
cites work: Q4039740
cites work: Q5802854
cites work: Integral equations with decreasing nonlinearities and applications
cites work: Q5624798
cites work: Q4121501
cites work: On finite displacements of circular elastic membranes
cites work: Stable and Unstable Axisymmetric Solutions for Membranes of Revolution
description: scientific article; zbMATH DE number 63812