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Computation of Imperfection‐Sensitivity at Two‐Fold Branching Points
Author(s) -
Gáspár Z.
Publication year - 1983
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19830630804
Subject(s) - bifurcation , mathematics , computation , degenerate energy levels , branching (polymer chemistry) , bifurcation theory , critical point (mathematics) , sensitivity (control systems) , mathematical analysis , nonlinear system , algorithm , physics , engineering , quantum mechanics , electronic engineering , materials science , composite material
There is a degenerate critical point ( usually elliptic or hyperbolic umbilic ) of the potential function of semisymmetric conservative systems in the case of a two‐fold branching point. The bifurcation set of a standard form is known in both cases in a parametrized form. In an imperfection‐sensitivity examination the relevant critical point is regarded as the first one reached by a continuously changing load, starting from a stable equilibrium state. The coordinate system of the imperfection‐sensitivity surface is transformed so that it coincides with a part of the bifurcation set of the standard form. Analysis of this reveals imperfections which decrease the critical load. Algorithms are given to compute these decreases. Finally the different possible forms of the equilibrium paths are sketched.