A nonlinear eigenvalue problem governing the eversion of elastic spherical caps
type: Item
instance of: scholarly article
title: A nonlinear eigenvalue problem governing the eversion of elastic spherical caps
zbMATH Open document ID: 0762.73037
DOI: 10.1007/BF01766301
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1992-09-27T00:00:00Z
review text: A nonlinear eigenvalue problem for a system of two ordinary differential equations describing the statical equilibrium of a thin elastic spherical cap is treated using the variational formulation. The everted equilibrium shapes of the spherical cap exist under certain conditions involving the relative magnitudes of the geometrical parameters characterizing the cap. The non-trivial solutions of the studied nonlinear eigenvalue problem can be obtained as extremals of certain functional. A refined form of the steepest descent method is applied to follow the complete path of the solution. The characterization of the spectrum and the correspondent path of the solutions are given with the help of an extension technique.
Mathematics Subject Classification ID: 74G99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 49R50
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 47J10
Mathematics Subject Classification ID: 58C40
zbMATH DE Number: 59773
zbMATH Keywords: bifurcation
zbMATH Keywords: statical equilibrium
zbMATH Keywords: variational formulation
zbMATH Keywords: steepest descent method
zbMATH Keywords: extension technique
author: M. Rosati
reviewed by: István Ecsedi
MaRDI profile type: Publication
cites work: Q5820027
cites work: Bifurcation buckling of spherical caps
cites work: Axisymmetric buckling of hollow spheres and hemispheres
cites work: Les equations de von Kármán
cites work: A general study of nonlinear problems with three solutions in Hilbert spaces
cites work: Equilibrium of an Elastic Spherical Cap Pulled at the Rim
cites work: Numerical analysis for eversion in elastic spherical caps equilibrium
cites work: Q3847203
cites work: Q3336252
cites work: Q4146134
cites work: Q3948194
cites work: Q3749777
cites work: Path following near bifurcation
cites work: Q3666153
description: scientific article; zbMATH DE number 59773