Global properties of buckled states of plates that can suffer thickness changes
type: Item
instance of: scholarly article
title: Global properties of buckled states of plates that can suffer thickness changes
zbMATH Open document ID: 0698.73035
DOI: 10.1007/BF00873493
author: Stuart S. Antman
published in: Archive for Rational Mechanics and Analysis
publication date: 1990-01-01T00:00:00Z
review text: This paper is an extension of the work of the author on global buckling properties of nonlinearly elastic rods [e.g.: ibid. 84, 293-305 (1984; Zbl 0533.73042)] to the axisymmetric buckling of circular plates. Making use of the Cosserat theory the plates can suffer not only flexure, midplane extension and shear but also thickness changes. In addition the material of the plate is described by a very general system of nonlinear constitutive equations for elastic materials. The main result of the paper is the presentation of global bifurcation properties by determining the nodal properties of the solutions, which distinguish the branches globally.
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 4145443
zbMATH Keywords: axisymmetric deformation
zbMATH Keywords: circular plates
zbMATH Keywords: Cosserat theory
zbMATH Keywords: flexure
zbMATH Keywords: midplane extension
zbMATH Keywords: shear
zbMATH Keywords: thickness changes
zbMATH Keywords: general system of nonlinear constitutive equations for elastic materials
zbMATH Keywords: global bifurcation properties
zbMATH Keywords: nodal properties of the solutions
reviewed by: Hans Troger
MaRDI profile type: Publication
cites work: Existence and nonuniqueness of axisymmetric equilibrium states of nonlinarly elastic shells
cites work: Nonuniqueness of equilibrium states for bars in tension
cites work: Ordinary differential equations of non-linear elasticity. I: Foundations of the theories of non-linearly elastic rods and shells
cites work: Buckled states of nonlinearly elastic plates
cites work: Shear and necking instabilities in nonlinear elasticity
cites work: The remarkable nature of radially symmetric equilibrium states of aeolotropic nonlinearly elastic bodies
cites work: The principle of virtual work and integral laws of motion
cites work: The Intricate Global Structure of Buckled States of Compressible Columns
cites work: Structured phase transitions on a finite interval
cites work: Nonlinear Theory of Elastic Directed Surfaces
cites work: Necking and drawing in polymeric fibers under tension
cites work: On the cold drawing of polymers
cites work: The thermodynamics of elastic materials with heat conduction and viscosity
cites work: Bifurcation from simple eigenvalues
cites work: Equilibrium of bars
cites work: Special Topics in Elastostatics
cites work: Exact theory of stress and strain in rods and shells
cites work: Large thermal buckling of nonuniform beams and plates
cites work: Singular global bifurcation problems for the buckling of anisotropic plates
cites work: Existence and stability of necking deformations for nonlinearly elastic rods
cites work: Some global results for nonlinear eigenvalue problems
description: scientific article; zbMATH DE number 4145443