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

Cover image for Vol. 92 Issue 9

September 2012

Volume 92, Issue 9

Pages 597–766

  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
    8. Original Paper
    1. You have free access to this content
      Cover Picture: ZAMM 9/2012

      Version of Record online: 3 SEP 2012 | DOI: 10.1002/zamm.201290017

  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
    8. Original Paper
    1. You have free access to this content
      Issue Information: ZAMM 9 / 2012

      Version of Record online: 3 SEP 2012 | DOI: 10.1002/zamm.201290018

  3. Contents

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review
    8. Original Paper
    1. You have free access to this content
      Contents: ZAMM 9 / 2012 (pages 597–598)

      Version of Record online: 3 SEP 2012 | DOI: 10.1002/zamm.201209209

  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
    8. Original Paper
    1. Retrospective

      You have free access to this content
      Prandtl-Tomlinson model: History and applications in friction, plasticity, and nanotechnologies (pages 683–708)

      V.L. Popov and J.A.T. Gray

      Version of Record online: 5 JUL 2012 | DOI: 10.1002/zamm.201200097

      Thumbnail image of graphical abstract

      One of the most popular models widely used in nanotribology as the basis for many investigations of frictional mechanisms on the atomic scale is the so-called Tomlinson model consisting of a point mass driven over a periodic potential. The name “Tomlinson model” is, however, historically incorrect. This model should be better the “Prandtl-Tomlinson model”, or simply and rightly be dubbed the “Prandtl model”. The original paper by Ludwig Prandtl was written in German and was not accessible for a long time for the largest part of the international tribological community. Here is published a historical introduction and the English translation of the classical paper by Ludwig Prandtl.

  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
    8. Original Paper
    1. The decomposed form of the stress state for transversely isotropic beam bending based on elastic theory (pages 709–715)

      Y. Gao

      Version of Record online: 22 MAY 2012 | DOI: 10.1002/zamm.201100125

      The author studies a plane stress problem of rectangular beams which are slender and thin elastic bodies with free upper and lower surfaces and in the absence of body forces. Without employing ad hoc stress assumptions, the decomposed form of the stress state for transversely isotropic beam bending is proposed on the basis of the classical elastic theory, and the corresponding decomposition theorem is inextenso presented for the first time. It is shown that the stress state of transversely isotropic beams with free faces can be uniquely decomposed into two parts: the interior state and the Papkovich-Fadle (P-F) state.

    2. Asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity (pages 716–730)

      H. Itou, A.M. Khludnev, E.M. Rudoy and A. Tani

      Version of Record online: 22 MAY 2012 | DOI: 10.1002/zamm.201100157

      The authors consider an asymptotic behaviour of a solution near a tip of a rigid line inclusion in two dimensional homogeneous isotropic linearized elasticity. By means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution around there. Furthermore, they give expressions of the invariant integral and the Irwin's formula.

    3. Characteristic directions of closed planar motions (pages 731–748)

      H. Dathe and R. Gezzi

      Version of Record online: 22 MAY 2012 | DOI: 10.1002/zamm.201100178

      Thumbnail image of graphical abstract

      The authors investigate some properties of closed planar motions. For practical applications such as in biomechanics, the Steiner circle reduces to a straight line. After the mathematical study of the problem, finally, they show how the results can be applied to experimentally measured motions. The most important part of this motion is described as a double hinge driven by the hip and knee angle, which is a simple model for a planar motion. They conclude that the Steiner line allows us to visualize a selected direction of motion under consideration.

      Corrected by:

      Addendum: Addenda and Erratum to: Characteristic directions of closed planar motions

      Vol. 94, Issue 6, 551–554, Version of Record online: 27 JAN 2014

  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
    8. Original Paper
  7. Original Paper

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Book Review
    8. Original Paper
    1. Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions (pages 749–766)

      A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, R.M.N. Jorge and C.M.M. Soares

      Version of Record online: 25 MAY 2012 | DOI: 10.1002/zamm.201100186

      Thumbnail image of graphical abstract

      A hyperbolic sine shear deformation theory is used for the linear buckling analysis of functionally graded plates. The theory accounts for through-the-thickness deformations. The buckling governing equations and boundary conditions are derived using Carrera's Unified Formulation and further interpolated by collocation with radial basis functions. The collocation method is truly meshless, allowing a fast and simple discretization of equations in the domain and on the boundary. Numerical results demonstrate the high accuracy of the present approach.

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