Showing papers on "Infinite-period bifurcation published in 1979"

Non-normality and bifurcation in plane strain tension and compression

Abstract: T he bifurcations of a rectangular block subject to plane strain tension or compression are investigated. The block material is taken to be incompressible and is characterized by an incrementally linear constitutive law for which “normality” does not necessarily hold. The consequences of non-normality regarding bifurcation are given primary emphasis here. The characteristic regimes of the governing equations (elliptic, parabolic and hyperbolic) are detennined. In each of these regimes both symmetric and antisymmetric diffuse bifurcation modes are available. Additionally, in the hyperbolic and parabolic regimes, bifurcation into a localized shear band mode is also possible. Particular attention is given to the limiting cases of long wavelength and soon wavelength diffuse bifurcation modes. The range of parameter values is identified for which bifurcation into some localized mode may precede bifurcation into a long wavelength diffuse mode. Some difficulties associated with employing a linear incremental solid in a bifurcation analysis, when primary interest is in the bifurcation of an underlying elastic-plastic solid, are also discussed.

On the bifurcation diagram of discrete analogues for ordinary bifurcation problems

Abstract: Ordinary bifurcation problems of the form (1) typically have at most one nontrivial, nonnegative solution for λ > 0. The paper shows that this is in general not true for discrete analogues to (1) no matter how small the step width h > 0 is chosen.

Secondary Bifurcation and Multiple Eigenvalues

Abstract: Secondary bifurcation of general nonlinear operator equations is studied in the neighborhood of multiple eigenvalues of the linearized problem. Necessary conditions for the existence of secondary bifurcation are derived and the location of points of secondary bifurcation are found. The geometrical significance of these conditions is discussed and conditions on primary bifurcation at a multiple eigenvalue are found which guarantee the existence of points of secondary bifurcation.