An application of singularity theory to a bifurcation problem

DOI10.1007/BF02925002zbMath0554.73039MaRDI QIDQ3217701

Giuseppe Geymonat

Publication date: 1982

Published in: Rendiconti del Seminario Matematico e Fisico di Milano (Search for Journal in Brave)

zbMATH Keywords

singularity theorypost-buckling behaviorpolygonal cross-sectionnonlinearly hyperelastic thin rodreduction of the bifurcation problem to a two-dimensional one

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Bifurcation and buckling (74G60) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Cites Work

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• Post-buckling behavior of a nonlinearly hyperelastic thin rod with cross- section invariant under the dihedral group \(D_ n\)
• Imperfect bifurcation in the presence of symmetry
• Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity
• Smooth functions invariant under the action of a compact Lie group
• Singularites \(C^\infty\) en presence de symétrie. En particulier en presence de la symétrie d'un groupe de Lie compact
• On differentiable functions with isolated critical points
• A splitting lemma for non-reflexive Banach spaces.
• Variational and topological methods in nonlinear problems
• A theory for imperfect bifurcation via singularity theory
• Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids

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