Multimode bifurcations of elastic equilibria

DOI10.1016/0021-8928(88)90015-9zbMath0717.73038OpenAlexW2083641537MaRDI QIDQ2638855

Yu. I. Sapronov

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0021-8928(88)90015-9

zbMATH Keywords

Lyapunov-Schmidt methodbreaking of symmetrytotal energy functionalRitz approximationscascade bifurcationsConservative elastic systemsfundamental bifurcation modesparallelepiped symmetrypostcritical equilibriasoft bucklingsymmetric matrix with non-degenerate principle (diagonal) minors

Mathematics Subject Classification ID

Bifurcation and buckling (74G60) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Cites Work

• On adjacencies of singularities \(A_ k\) to points of the \(\mu =const\) stratum of a singularity
• Lyapunov stability and sign definiteness of a quadratic form in a cone
• Imperfect bifurcation in the presence of symmetry
• Secondary edge effect in the bending of thin elastic shells
• Singularites \(C^\infty\) en presence de symétrie. En particulier en presence de la symétrie d'un groupe de Lie compact
• SINGULARITIES OF FUNCTIONS ON BOUNDARIES, CORNERS, ETC.
• Boundary Conditions and Mode Jumping in the von Kármán Equations
• A Second note on Symmetry of Singularities
• Group Representation Theory and Branch Points of Nonlinear Functional Equations
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