ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

Cover image for Vol. 94 Issue 3

March 2014

Volume 94, Issue 3

Pages 185–272

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review
    1. You have free access to this content
      Cover Picture: ZAMM 3 / 2014

      Article first published online: 3 MAR 2014 | DOI: 10.1002/zamm.201490003

  2. Issue Information

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review
    1. You have free access to this content
      Issue Information: ZAMM 3 / 2014

      Article first published online: 3 MAR 2014 | DOI: 10.1002/zamm.201490004

  3. Contents

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review
    1. You have free access to this content
      Contents: ZAMM 3 / 2014 (pages 185–186)

      Article first published online: 3 MAR 2014 | DOI: 10.1002/zamm.201409403

  4. Editor's Choice

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review
    1. You have free access to this content
      The Prandtl-Reuss equations revisited (pages 187–202)

      O.T. Bruhns

      Article first published online: 25 NOV 2013 | DOI: 10.1002/zamm.201300243

      At the beginning of the last century two different types of constitutive relations to describe the complex behavior of elastoplastic material were presented. These were the deformation theory originally developed by Hencky and the Prandtl-Reuss theory. Whereas the former provides a direct solid-like relation of stress as function of strain, the latter has been based on an additive composition of elastic and plastic parts of the increments of strains. These in turn were taken as a solid- and fluid-like combination of the de Saint-Venant/Lévy theory with an incremental form of Hooke's law. Even nowadays this Prandtl-Reuss theory is still accepted within the restriction of small elastic deformations. In the present article it is shown that this restrictive statement may be no longer true. Introducing a specific objective time derivative it could be shown that these defects disappear.

  5. Original Papers

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review
    1. Small-amplitude grain boundaries of arbitrary angle in the Swift-Hohenberg equation (pages 203–232)

      A. Scheel and Q. Wu

      Article first published online: 18 FEB 2013 | DOI: 10.1002/zamm.201200172

      The authors study grain boundaries in the Swift-Hohenberg equation. Grain boundaries arise as stationary interfaces between roll solutions of different orientations. Their analysis shows that such stationary interfaces exist near onset of instability for arbitrary angles between the roll solutions. This extends prior work in [Haragus and Scheel, see below] where the analysis was restricted to large angles, that is, weak bending near the grain boundary. The main new difficulty stems from possible interactions of the primary modes with other resonant modes. They generalize the normal form analysis in [M. Haragus and A. Scheel, Europ. J. Appl. Math. 23, 737–759 (2012)] and develop a singular perturbation approach to treat resonances.

    2. Properties and simplifications of constitutive time-discretized elastoplastic operators (pages 233–255)

      S. Sysala

      Article first published online: 22 FEB 2013 | DOI: 10.1002/zamm.201200056

      In the paper, a general constitutive elastoplastic model for associated plasticity is investigated. The model is based on the thermodynamical framework with internal variables and can include basic plastic criteria with a combination of kinematic hardening and non-linear isotropic hardening. The corresponding initial value constitutive elastoplastic problem is discretized by the implicit Euler method. The introduced simplifications are useful for a numerical implementation and can be used for deriving other properties like strong semismoothness of the elastoplastic operators for the classical plastic criteria or strong monotonicity of the stress-strain operator for some models with hardening. The derived properties can be important for convergence analyses of Newton-like methods and other mathematical and numerical analyses.

    3. Adaptive fuzzy sliding mode control of a chaotic pendulum with noisy signals (pages 256–263)

      W.M. Bessa, A.S. de Paula and M.A. Savi

      Article first published online: 25 FEB 2013 | DOI: 10.1002/zamm.201200214

      Thumbnail image of graphical abstract

      Chaotic response is related to a dense set of unstable periodic orbits (UPOs) and the system often visits the neighborhood of each one of them. In this work, an adaptive fuzzy sliding mode controller is combined with the close return method for the stabilization of UPOs in a chaotic pendulum. The adaptive fuzzy inference system is embedded in a smooth sliding mode controller to cope with both structured and unstructured uncertainties. Numerical results are presented in order to illustrate the ability of the proposed control scheme to track UPOs even in the presence of modeling inaccuracies and noisy input signals.

    4. The two-component Camassa-Holm system in weighted Lp spaces (pages 264–272)

      M. Kohlmann

      Article first published online: 8 APR 2013 | DOI: 10.1002/zamm.201200228

      The author presents some new persistence results for the non-periodic two-component Camassa-Holm (2CH) system in weighted Lp spaces. Working with moderate weight functions that are commonly used in time-frequency analysis, the paper generalizes some recent persistence results for the Camassa-Holm equation [L. Brandolese, Int. Math. Res. Not. 22, 5161–5181 (2012)] to its supersymmetric extension.

  6. Book Review

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review

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