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Titlebook: Imperfect Bifurcation in Structures and Materials; Engineering Use of G Kiyohiro Ikeda,Kazuo Murota Textbook 20021st edition Springer Scien

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0066-5452 a modern view of bifurcatoin theory by minimizing mathematicMany physical systems lose or gain stability and pattern through bifurca­ tion behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation be­ havior, for example,
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Echelon-Mode Formationand deformation size. The echelon mode can, for example, be found in various materials: soils (e.g., Ikeda, Murota, and Nakano, 1994 [92]), rocks (e.g., Pollard, Segal, and Delaney, 1982 [151]; Davis, 1984 [35]; Petit, 1988 [147]), and metals (e.g., Bai and Dodd, 1992 [10]; Duszek—Perzyna and Perzyna, 1993 [42]; Poirier, 1985 [150]).
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Group-Theoretic Bifurcation Theorya neighborhood of each critical point can be thoroughly investigated by the Liapunov—Schmidt reduction. One of the most important findings of this theory is that the rule of such bifurcation does not depend on the individual material or physical properties but merely on the symmetry of the system under consideration.
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Bifurcation of Steel Specimensfurcation as the direct bifurcation from a uniform state. Computational studies have also been conducted to simulate the direct bifurcation leading to shear-band formation (Tvergaard, Needleman, and Lo, 1981 [182]; Tvergaard and Needleman, 1984 [181]; Petryk and Thermann, 1992 [148]).
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Textbook 20021st editionelds of science and engineering. The study of dynamic bifurcation be­ havior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-b
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Bifurcation Behavior of D,-Equivariant SystemsD.- and C.-equivariant systems, emphasis naturally is to be placed on the double bifurcation points, because most of the results in Chapters 2 and 3 are applicable to the simple critical points of these systems.
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Textbook 20021st editionf the strength of structural systems by initial imperfections is formulated as im­ perfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statis­ tical variation of initial imperfections. A difficulty in these
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