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

Cover image for Vol. 94 Issue 1‐2

Special Issue: Refined theories of plates and shells

January 2014

Volume 94, Issue 1-2

Pages 1–184

Issue edited by: Victor A. Eremeyev, Wojciech Pietraszkiewicz

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choices
    7. Original Papers
    8. Book Review
    9. Original Paper
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      Cover Picture: ZAMM 1–2 / 2014

      Article first published online: 7 JAN 2014 | DOI: 10.1002/zamm.201490001

      Thumbnail image of graphical abstract

      Buckling mode of simply supported cylindrical shell subjected to uniform temperature rise, see Stanislav V. Levyakov and Viktor V. Kuznetsov, this issue, pp. 113.

  2. Issue Information

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

      Article first published online: 7 JAN 2014 | DOI: 10.1002/zamm.201490002

  3. Contents

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

      Article first published online: 7 JAN 2014 | DOI: 10.1002/zamm.201409401

  4. Editorial

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choices
    7. Original Papers
    8. Book Review
    9. Original Paper
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      Editorial: Refined theories of plates and shells (pages 5–6)

      V.A. Eremeyev and W. Pietraszkiewicz

      Article first published online: 5 AUG 2013 | DOI: 10.1002/zamm.201300148

  5. Editor's Choices

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choices
    7. Original Papers
    8. Book Review
    9. Original Paper
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      Classical plate buckling theory as the small-thickness limit of three-dimensional incremental elasticity (pages 7–20)

      D.J. Steigmann and R.W. Ogden

      Article first published online: 19 NOV 2012 | DOI: 10.1002/zamm.201200160

      Classical plate buckling theory is obtained systematically as the small-thickness limit of the three-dimensional linear theory of incremental elasticity with null incremental data. Various a priori assumptions associated with classical treatments of plate buckling, including the Kirchhoff–Love hypothesis, are here derived rather than imposed, and the conditions under which they emerge are stated precisely.

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      Modeling of consistent second-order plate theories for anisotropic materials (pages 21–42)

      P. Schneider, R. Kienzler and M. Böhm

      Article first published online: 28 FEB 2013 | DOI: 10.1002/zamm.201100033

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      By Fourier-series expansion in thickness direction of the plate with respect to a basis of scaled Legendre polynomials, several equivalent (and therefore exact) two-dimensional formulations of the three-dimensional boundary-value problem of linear elasticity in weak formulation for a plate with constant thickness are derived. These formulations are sets of countably many PDEs, which are power series in the squared plate parameter.

  6. Original Papers

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choices
    7. Original Papers
    8. Book Review
    9. Original Paper
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      Optimization of concrete shells using genetic algorithms (pages 43–54)

      G. Bertagnoli, L. Giordano and S. Mancini

      Article first published online: 17 JUN 2013 | DOI: 10.1002/zamm.201200215

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      The authors address the Skew Reinforcement Design in Reinforced Concrete Two Dimensional Elements. It consists of determining the minimum reinforcement required to respect all the constraints given by the geometric properties and the internal actions working on it. As this problem is strongly nonlinear and non-convex it cannot be easily solved using exact methods, while heuristics and meta-heuristics are suitable to this purpose. The authors propose a Genetic Algorithm (GA) and an enhanced version of it. They report computational results showing both the effectiveness of the proposed method, and the benefit of combining GAs with intensification methods.

      Within the framework as used in the preceeding paper the semi-classical black hole bound on the number of particle species Nspecies is revised. It is shown that unlike the bound on global charge, the bound on species survives in the quantum picture and gives rise to a new fundamental length-scale, beyond which the resolution of species identities is impossible. This finding nullifies the so-called species problem. This scale sets the size of the lightest quantum black hole in the theory, the Planckion.

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      On the bending of plates in the electromagnetic theory of microstretch elasticity (pages 55–71)

      C. Galeş and N. Baroiu

      Article first published online: 18 FEB 2013 | DOI: 10.1002/zamm.201200219

      This paper deals with the electromagnetic theory of microstretch elasticity. The full dynamic theory, which describes the interaction of electromagnetic fields with piezoelectric bodies, called piezoelectromagnetism, is considered. First, the authors derive the equations governing the bending theory of thin piezoelectromagnetic microstretch plates. Then, the boundary initial value problem is formulated and a uniqueness result is presented. Finally, the effects of a concentrated charge density in an infinite plate are studied.

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      Enhanced functionally graded material shell finite elements (pages 72–84)

      S. Kugler, P.A. Fotiu and J. Murin

      Article first published online: 18 MAR 2013 | DOI: 10.1002/zamm.201200183

      Structures made of Functionally Graded Materials (FGMs) show a gradual variation of material properties in one, two, or three directions. In this paper, an efficient low-order shell element with six nodal degrees of freedom (including the drill rotation) is presented, supplemented with a proper method for calculating effective elastic properties. This new FGM shell element can be coupled with 3D FGM beam elements on a single node. The numerical results indicate high effectiveness and accuracy of the proposed approach.

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      Refined modeling of composite plates with in-plane heterogeneity (pages 85–100)

      C.-Y. Lee, W. Yu and D.H. Hodges

      Article first published online: 8 APR 2013 | DOI: 10.1002/zamm.201200209

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      This article is concerned with the mechanical behavior of heterogeneous composite plates with elastic moduli and layered geometries varying through the thickness direction and periodically along the in-plane directions.

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      Nonlinear stability analysis of functionally graded shells using the invariant-based triangular finite element (pages 101–117)

      S.V. Levyakov and V.V. Kuznetsov

      Article first published online: 2 JUL 2013 | DOI: 10.1002/zamm.201200188

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      The paper discusses a finite-element approach for nonlinear analysis of thermal buckling and postbuckling behaviors of plates and shells fabricated of functionally graded materials. The triangular finite-element is formulated using representation of the strain energy as a function of invariants of the membrane, bending, and transverse shear strains. The invariants are expressed in terms of the strain tensor components determined in the direction of the element edges, which provides some computational benefits.

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      Equilibrium equations for transversely accreted shells (pages 118–129)

      S. Lychev

      Article first published online: 10 JUN 2013 | DOI: 10.1002/zamm.201200231

      A particular case of the theory of growing thin-walled structures, namely the theory of transversely accreted shells is considered. A correspondence between equilibrium equations in terms of rates for transversally accreted shells and equilibrium equations in terms of displacements for permanent shells is established. The equilibrium equations for accreted shells that obey the kinematics hypothesis of Mindlin type are derived in terms of displacements as well as in terms of rates.

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      On localized modes of free vibrations of single-walled carbon nanotubes embedded in nonhomogeneous elastic medium (pages 130–141)

      G. Mikhasev

      Article first published online: 21 JAN 2013 | DOI: 10.1002/zamm.201200140

      Free axisymmetric vibrations of a single-walled carbon nanotube (SWCNT) embedded in a nonhomogeneous elastic matrix are studied on the base of the nonlocal continuum shell theory. The effect of the surrounding elastic medium are considered using the Winkler-type spring constant which is assumed to be variable along the tube axis. The tube may be prestressed by external tensile forces. The Flügge type shell equations, including the initial membrane hoop and axial stresses, are used as the governing ones. The constitutive equations are formulated by considering the small-scale effects. Using the asymptotic approach, the SWCNT eigenmodes are constructed in the form of functions decreasing rapidly away from some “weakest” line which is assumed to be far from the tube edges. The dependence of the natural frequencies and the power of the localization of the corresponding modes upon the constant of non-locality, tensile stresses and the nanotube radius is analyzed.

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      Concerning one approach to the reconstruction of heterogeneous residual stress in plate (pages 142–149)

      R. Nedin and A. Vatulyan

      Article first published online: 18 FEB 2013 | DOI: 10.1002/zamm.201200195

      In present paper the inverse problem on the identification of three non-homogeneous residual stress components in rectangular plate in steady-state vibration regime is considered. The equation building the iterative process of solving the inverse problem is formulated. An approach to the reconstruction of residual stresses is described on the basis of introduction the Airy prestress function. The technique of leading the inverse problem to a system of linear algebraic equations at each iteration is proposed. Results of conducting a series of computational experiments on the reconstruction are depicted and discussed.

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      Finite element modeling of Kirchhoff-Love shells as smooth material surfaces (pages 150–163)

      Yu. Vetyukov

      Article first published online: 17 DEC 2012 | DOI: 10.1002/zamm.201200179

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      The author considers large deformations of curved thin shells in the framework of a classical Kirchhoff-Love theory for material surfaces. The geometry of the element is approximated via the position vector and its derivatives with respect to the material coordinates at the four nodes, and C1 continuity of the surface over the interfaces between the elements is guaranteed. Theoretical background provides certainty concerning the boundary conditions, the range of applicability of the model, extensions to multi-field problems, etc. Robust convergence and accuracy of the resulting simple numerical scheme is demonstrated by the analysis of benchmark problems in comparison with other solutions.

  7. Book Review

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choices
    7. Original Papers
    8. Book Review
    9. Original Paper
    1. You have free access to this content
  8. Original Paper

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choices
    7. Original Papers
    8. Book Review
    9. Original Paper
    1. You have free access to this content
      A Vekua-type linear theory of thick elastic shells (pages 164–184)

      S. Zhavoronok

      Article first published online: 2 JUL 2013 | DOI: 10.1002/zamm.201200197

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      This paper presents an effective variational formalism of construction of the thick anisotropic linear shell theory of Vekua-type of an arbitrary order. The dynamic equations are formulated as the Lagrange equations of the second kind, independent from expansion functions. The asymmetric stress tensor is used to obtain the compact form of the dynamic equations similar to the classical shell theories. The proposed approach allows one for computer-aided derivation of all equations using computer algebra software supporting main tensor operations. Some solutions of test problems are presented.

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