Pitchfork and octopus bifurcations in a hyperelastic tube subjected to compression: Analytical post-bifurcation solutions and imperfection sensitivity

DOI10.1177/1081286514543597zbMath1327.74064OpenAlexW2052193726MaRDI QIDQ2950688

Jian Xu, Jiong Wang, Fan-Fan Wang, Hui-Hui Dai

Publication date: 9 October 2015

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://opus4.kobv.de/opus4-fau/files/8223/Dai_Pitchfork.pdf

zbMATH Keywords

asymptotic analysisimperfection sensitivityhyperelasticitytubepost-bifurcation solutions

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Bifurcation and buckling (74G60)

Related Items (4)

A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates ⋮ An asymptotic modeling and resolution framework for morphology evolutions of multiple-period post-buckling modes in bilayers ⋮ Buckling and post-buckling of a compressible slab under combined axial compression and lateral load ⋮ Computing wrinkling and restabilization of stretched sheets based on a consistent finite-strain plate theory

Cites Work

• An analytical study on the instability phenomena during the phase transitions in a thin strip under uniaxial tension
• Stability and bifurcation of compressed elastic cylindrical tubes
• Asymmetric bifurcations of thick-walled circular cylindrical elastic tubes under axial loading and external pressure
• Bifurcation of inflated circular cylinders of elastic material under axial loading - II. Exact theory for thick-walled tubes
• Imperfect bifurcation in the presence of symmetry
• Bifurcation of inflated circular cylinders of elastic material under axial loading - I. Membrane theory for thin-walled tubes
• Cylindrical shell buckling: a characterization of localization and periodicity
• Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods
• Elliptic-Spline Solutions for Large Localizations in a Circular Blatz–Ko Cylinder Due to Geometric Softening
• ANALYTICAL SOLUTIONS FOR THE POST-BUCKLING STATES OF AN INCOMPRESSIBLE HYPERELASTIC LAYER
• Phase transitions in a slender cylinder composed of an incompressible elastic material. I. Asymptotic model equation
• Asymptotic bifurcation analysis and post-buckling for uniaxial compression of a thin incompressible hyperelastic rectangle
• Instability of a Bell Constrained Cylindrical Tube Under end Thrust-Part 1: Theoretical Development
• Instability of a Bell Constrained Cylindrical Lhbe Under end Thrust-Part 2: Examples, Thin Libe Analysis
• Asymptotic Bifurcation Solutions for Compressions of a Clamped Nonlinearly Elastic Rectangle: Transition Region and Barrelling to a Corner-like Profile
• Nonlinear Euler buckling
• Imperfection Sensitivity of Externally Pressurized Spherical Shells
• ON THE STABILITY OF A CIRCULAR TUBE UNDER END THRUST

This page was built for publication: Pitchfork and octopus bifurcations in a hyperelastic tube subjected to compression: Analytical post-bifurcation solutions and imperfection sensitivity