Analysis of post‐buckling branches at multiple symmetric bifurcations

DOI10.1002/nme.157zbMath0997.74022OpenAlexW2043901459MaRDI QIDQ2729294

Anders Magnusson

Publication date: 14 November 2002

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.157

zbMATH Keywords

finite elementasymptotic expansion methodbifurcation equationsLyapunov-Schmidt theoryKoiter linessymmetric multiple bifurcations

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Finite element methods applied to problems in solid mechanics (74S05) Bifurcation and buckling (74G60)

Uses Software

• CALFEM

Cites Work

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• A homotopy for solving general polynomial systems that respects m- homogeneous structures
• A quadratically convergent procedure for the calculation of stability points in finite element analysis
• Secondary bifurcations in the buckling problem
• Postbuckling behavior and imperfection sensitivity of elastic structures by the Lyapunov-Schmidt-Koiter approach
• Multiple path generation at coincident branching points
• Generalized Deflated Block-Elimination
• The Computation of Symmetry-Breaking Bifurcation Points
• Secondary Bifurcation Near a Double Eigenvalue
• A fast incremental/iterative solution procedure that handles “snap-through”
• On a Reduction Process for Nonlinear Equations
• An orthogonal residual procedure for non‐linear finite element equations
• Perturbed bifurcation theory

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