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

Cover image for Vol. 92 Issue 8

August 2012

Volume 92, Issue 8

Pages 597–680

  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 8/2012

      Article first published online: 3 AUG 2012 | DOI: 10.1002/zamm.201290014

  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 8 / 2012

      Article first published online: 3 AUG 2012 | DOI: 10.1002/zamm.201290015

  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 8 / 2012 (pages 597–598)

      Article first published online: 3 AUG 2012 | DOI: 10.1002/zamm.201209208

  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
      A higher-order finite element approach to the Kuramoto-Sivashinsky equation (pages 599–607)

      D. Anders, M. Dittmann and K. Weinberg

      Article first published online: 22 MAY 2012 | DOI: 10.1002/zamm.201200017

      Thumbnail image of graphical abstract

      The Kuramoto-Sivashinsky equation has emerged as a fundamental evolution equation to describe highly nonlinear physical processes in unstable systems. In general, it constitutes a nonlinear initial-valued problem involving fourth-order spatial derivatives. Finite element solutions for the Kuramoto-Sivashinsky equation are not common because the primal variational formulation of fourth-order operators requires finite element basis functions which are piecewise smooth and globally at least C1-continuous. In this paper a novel B-spline based finite element approach to the solution of the one-dimensional Kuramoto-Sivashinsky equation is presented. Extensive numerical studies of different scenarios in the Kuramoto-Sivashinsky equation will illustrate the quality of our approach.

  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. Microstructure-based modelling and FE implementation of filler-induced stress softening and hysteresis of reinforced rubbers (pages 608–631)

      H. Lorenz, M. Klüppel and G. Heinrich

      Article first published online: 22 MAY 2012 | DOI: 10.1002/zamm.201100172

      Thumbnail image of graphical abstract

      Reinforcement of rubber by nanoscopic fillers induces strong nonlinear mechanical effects such as stress softening and hysteresis. The proposed model aims to describe these effects on a micromechanical level in order to predict the stress-strain behaviour of a rubber compound. The material parameters can be obtained by fitting stress-strain tests. The previously introduced “dynamic flocculation model” was extended for general deformation histories. Stress softening is modelled by hydrodynamic reinforcement of rubber elasticity due to strain amplification by stiff filler clusters. Hysteresis is attributed to cyclic breakdown and re-aggregation of damaged clusters. When stressstrain cycles are not closed, not all of these clusters are broken at the turning points. For the resulting “inner cycles” additional elastic stress contributions of clusters are taken into account. The uniaxial model has been generalized for threedimensional stress states using the concept of representative directions. The resulting 3D-model was implemented into a Finite Element code, and an example simulation is shown. Good agreement between measurement and simulation is obtained for uniaxial inner cycles, while the 3D-generalization simulates the behaviour closer to the experiment than the original model.

    2. Basic solution of four 3-D rectangular limited-permeable cracks in piezoelectric materials (pages 632–651)

      J.-Y. Liu, Z.-G. Zhou and B.-B. Zhou

      Article first published online: 19 APR 2012 | DOI: 10.1002/zamm.201100106

      The solution of four 3-D rectangular limited-permeable cracks in piezoelectric materials were given by using the generalized Almansi's theorem and the Schmidt method. The effects of the electric permittivity of the air inside the rectangular crack, the shape of the rectangular crack and the distance among four rectangular cracks on the stress and electric displacement intensity factors in piezoelectric materials were analyzed.

    3. Non-linear analysis of moderately thick laminated plates and shell panels under thermo-mechanical loadings (pages 652–667)

      S. Maleki and M. Tahani

      Article first published online: 25 MAY 2012 | DOI: 10.1002/zamm.201100103

      Non-linear bending analysis of moderately thick laminated plates and cylindrical panels with various thermo-mechanical loadings and boundary conditions is presented using generalized differential quadrature (GDQ) method together with the Newton-Raphson iterative scheme. Different symmetric and asymmetric lamination sequences together with various combinations of clamped, simply supported and free boundary conditions are considered. Assuming the effects of shear deformation and initial curvature, based on the first-order shear deformation theory (FSDT) and von Kármán-type of geometric non-linearity, the governing system of equations is obtained.

    4. High accuracy postbuckling analysis of box section struts (pages 668–680)

      S.A.M. Ghannadpour, H.R. Ovesy and M. Nassirnia

      Article first published online: 22 MAY 2012 | DOI: 10.1002/zamm.201100121

      Thumbnail image of graphical abstract

      This paper presents the theoretical developments of two finite strip methods (i.e. semi-analytical and full-analytical) for the post-buckling analysis of some box section struts. The investigation of struts buckling behaviour is then extended to the post-buckling study with the assumption that the deflected form after the buckling is the combination of first, second and higher (if required) modes of buckling. Thus, the full-analytical post-buckling study is effectively a multi term analysis, which is attempted by utilizing the so-called semi-energy method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of these methods is significantly promoted.

  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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