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

Cover image for Vol. 92 Issue 10

October 2012

Volume 92, Issue 10

Pages 767–848

  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 Papers
    1. You have free access to this content
      Cover Picture: ZAMM 10/2012

      Article first published online: 1 OCT 2012 | DOI: 10.1002/zamm.201290020

  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 Papers
    1. You have free access to this content
      Issue Information: ZAMM 10 / 2012

      Article first published online: 1 OCT 2012 | DOI: 10.1002/zamm.201290021

  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 Papers
    1. You have free access to this content
      Contents: ZAMM 10 / 2012 (pages 767–769)

      Article first published online: 1 OCT 2012 | DOI: 10.1002/zamm.201209210

  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 Papers
    1. You have free access to this content
      Adaptive Gaussian particle method for the solution of the Fokker-Planck equation (pages 770–781)

      M.D. Scharpenberg and M. Lukáčová-Medviová

      Article first published online: 11 JUN 2012 | DOI: 10.1002/zamm.201100088

      Thumbnail image of graphical abstract

      The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE) or a deterministic ordinary differential equation (ODE) with stochastic initial values. A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the ODE. The decomposition as well as the propagation is subject to possibly large numerical errors due to the difficulty to control the spatial residual over the whole domain. In this paper a new particle method is derived, which allows a deterministic error control for the resulting probability density. It is based on global optimization and allows an adaption of an efficient surrogate model for the residual estimation.

  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 Papers
    1. The flexural vibration of V shaped atomic force microscope cantilevers by using the Timoshenko beam theory (pages 782–800)

      A. Sadeghi

      Article first published online: 22 MAY 2012 | DOI: 10.1002/zamm.201100100

      Thumbnail image of graphical abstract

      The resonant frequency of flexural vibration for a V shaped atomic force microscope (AFM) cantilever has been investigated using the Timoshenko beam theory. Generally, three different regions are considered for V shaped cantilevers, one region with constant cross section and height and two double tapered regions. In this paper, the effects of the different parameters on the non-dimensional frequency and sensitivity to the contact stiffness have been studied. The differential quadrature method (DQM) is applied to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when Timoshenko beam parameter or cantilever thickness increases and high order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the high order frequencies are sensitive to the contact stiffness in a larger range.

    2. On large-time energy concentration in solutions to the Navier-Stokes equations in the whole 3D space (pages 801–815)

      Z. Skalák

      Article first published online: 6 JUN 2012 | DOI: 10.1002/zamm.201000241

      In the first part of the paper the author studies the large-time behavior of the higher-order space derivatives of solutions to the Navier-Stokes equations in ℝ3. Specifically, they show that if w is a nonzero global weak solution to the Navier-Stokes equations satisfying the strong energy inequality and 0 < α < β < ∞, then there exist C = C(α,β) > 1, δ0 = δ0(α,β) ∈ (0,1) and t0 = t0(α,β) > 0 such that

      • equation image

      for every t > t0 and every δ ∈ [0,δ0]. A denotes the Stokes operator and Aβ its powers. In the second part of the paper the author derives several consequences of the above inequality concerning the large-time energy concentration in w.

    3. Exact and complete electro-elastic field in a half-space of piezoelectric medium with a charged surface electrode: Revisit (pages 816–823)

      X.Y. Li

      Article first published online: 11 JUN 2012 | DOI: 10.1002/zamm.201200015

      Thumbnail image of graphical abstract

      This note revisits the electro-elastic coupling behaviors of a transversely isotropic piezoelectric half-space with a charged surface electrode. A different idea is provided by employing the three-dimensional (3D) general solution of electroelasticity as well as generalized potential theory method. Compared with the previous studies, the method in this study is very simple and straightforward. The potential theory method is successfully extended to non-axisymmetric case and the electrode can be of any planar configuration. For a charged penny-shaped electrode, exact and complete 3D analysis is conducted.

  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 Papers
  7. 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 Papers
    1. On the measurement of surface tension and contact angle (pages 824–828)

      E. Miersemann

      Article first published online: 11 JUN 2012 | DOI: 10.1002/zamm.201200034

      The author proposes a new method which combines experiments with numerical calculations to determine the capillary constant and the capillary contact angle. He measures the ascent of the liquid at the interior and at the exterior of a circular transparent tube. In contrast to known methods we do not assume that the contact angle is known. Assuming the interior contact angle is equal to the exterior angle, he finds the capillary constant of the given liquid from the fact that the surface tensions of the interior and the exterior surfaces are equal. Dipping a cylindrical wire with constant circular cross section into a liquid with known surface tension we can determine the contact angle between the given liquid and the material from which the wire is made.

    2. Modelling strain localization by cohesive/overlapping zones in tension/compression: Brittleness size effects and scaling in material properties (pages 829–840)

      A. Carpinteri and M. Paggi

      Article first published online: 11 JUN 2012 | DOI: 10.1002/zamm.201200035

      Thumbnail image of graphical abstract

      The present paper is a state-of-the-art review of the research carried out at the Politecnico di Torino during the last two decades on the modelling of strain localization. Introducing the elementary cohesive/overlapping models in tension/compression, it will be shown that it is possible to get a deep insight into the ductile-to-brittle transition and into the scaling of the material properties usually detected when testing quasi-brittle material specimens or structures at different size-scales.

    3. Asymptotic modelling and design of some microlayered functionally graded heat conductors (pages 841–848)

      C. Woźniak, M. Wa̧growska and O. Szlachetka

      Article first published online: 5 JUL 2012 | DOI: 10.1002/zamm.201100092

      Thumbnail image of graphical abstract

      The paper presents a new method of modelling for certain microlayered heat conductors. The main future of the presented approach is that it can be also applied to the class with a non periodic structure. These structures can by referred to as functionally graded in the direction normal to the interfaces between layers. At the same time the non-homogenous material structure of the composite is slowly varying in this direction. That is why the obtained model equations have functionally but slowly varying coefficients. Moreover, this equations can by applied for designing functionally graded heat conductors with given a priori class of temperature fields.

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