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

Cover image for Vol. 91 Issue 12

December 2011

Volume 91, Issue 12

Pages 923–1008

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Comment
    8. Annual Index
    1. Cover Picture: ZAMM 12/2011

      Version of Record online: 8 NOV 2011 | DOI: 10.1002/zamm.201190025

  2. Issue Information

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Comment
    8. Annual Index
    1. Issue Information: ZAMM 12 / 2011

      Version of Record online: 8 NOV 2011 | DOI: 10.1002/zamm.201109115

  3. Contents

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Comment
    8. Annual Index
    1. Contents: ZAMM 12 / 2011 (pages 923–925)

      Version of Record online: 8 NOV 2011 | DOI: 10.1002/zamm.201109114

  4. Editor's Choice

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Comment
    8. Annual Index
    1. You have free access to this content
      Topological derivatives for networks of elastic strings (pages 926–943)

      G. Leugering and J. Sokolowski

      Version of Record online: 5 AUG 2011 | DOI: 10.1002/zamm.201000067

      Thumbnail image of graphical abstract

      The authors consider linear second order differential equations on metric graphs under given boundary and nodal conditions. They are interested in the problem of changing the topology of the underlying graph in that they replace a multiple node by a subgraph or concentrate a subgraph to a single node. They wish to do so in an optimal fashion. More precisely, given a cost function the authors may look for its sensitivity with respect to these operations in order to find an optimal topology of the graph. Thus, in essence, they are looking for the topological gradient for linear second order problems on metric graphs.

  5. Original Papers

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Comment
    8. Annual Index
    1. The homogenized equations of motion for an activated elastic lamination in plane strain (pages 944–956)

      W.C. Sanguinet

      Version of Record online: 21 JUN 2011 | DOI: 10.1002/zamm.201000208

      Thumbnail image of graphical abstract

      The paper begins by attempting to evaluate the materials' average Lagrangian (action density). In doing so, it immediately becomes apparent that expressions are needed for average momentum and stress. Both quantities are found to depend linearly on average strain and average velocity. After calculating the general Euler equations of motion, isotropy was assumed, and two additional forces (one being of a Coriolis nature) were found in the averaged equations of elastodynamics due to the presence of simultaneous change in both inertial and elastic properties of the original material constituents. The appearance of these two forces is a consequence of both dynamics and plane strain; the Coriolis type force disappears in the case ofone dimensional strain that arises when longitudinal dynamic disturbances propagate along an elastic bar.

    2. Optimization of a functionally graded circular plate with inner rigid thin obstacles. II. Approximate problems (pages 957–966)

      I. Hlaváček and J. Lovíšek

      Version of Record online: 21 JUN 2011 | DOI: 10.1002/zamm.201000238

      Optimal design of a simply supported functionally graded axisymmetric circular plate resting on several inner rigid rings is presented in Part I. The variable thickness and the exponent of the power-law of the grading function are to be optimized. In Part II the approximate state problem and approximate optimal design problems are introduced, using spaces of linear and cubic Hermite splines, respectively. The authors prove the existence of approximate solutions and the convergence of a subsequence of the solutions to a solution of the original continuous optimal design problem.

    3. Generalized self-consistent like method for mechanical degradation of fibrous composites (pages 967–978)

      D.P. Boso, M. Lefik and B.A. Schrefler

      Version of Record online: 5 JUL 2011 | DOI: 10.1002/zamm.201000209

      Thumbnail image of graphical abstract

      This paper deals with homogenization of heterogeneous, fibre-reinforced material. One of the main points of the work consists in taking into account the breakage of the fibres, to compute the effective behaviour of the damaged composite. Furthermore, the possible yielding of the matrix material is considered. The problem is solved for the coupled thermomechanical field, that is all material characteristics can be temperature dependent and thermal loads can be simulated. The method is based on a self consistent type scheme, suitably extended for the case at hand. On the contrary, in this work the solution is found in a non-classical way, as we use the finite element method to find the solution of the thermomechanical problem as a function of the effective material characteristics.

    4. The solution of system of integral differential equations and its application in the theory of elasticity (pages 979–992)

      N. Shavlakadze

      Version of Record online: 18 JUL 2011 | DOI: 10.1002/zamm.201000220

      Thumbnail image of graphical abstract

      A contact problem of the theory of elasticity of infinite compound and infinite orthotropic plates with an elastic semiinfinite or finite inclusion of variable rigidity is considered. The problem is reduced to the system of integral differential equations with variable coefficient of singular operator. If such coefficient varies with power law the author can manage to investigate the obtained equations, using the methods of analytical functions to get exact solutions and to establish behavior of unknown contact stresses at the ends of elastic inclusion. In some case using the method of orthogonal polynomials he obtains the dual infinite system of linear algebraic equations. The method of reduction for approximate solution is developed.

    5. On an iteration method of finding a solution of a nonlinear equilibrium problem for the Timoshenko plate (pages 993–1001)

      J. Peradze

      Version of Record online: 5 AUG 2011 | DOI: 10.1002/zamm.201100016

      Thumbnail image of graphical abstract

      A boundary value problem of Timoshenko plate equilibrium in axially symmetric displacements is considered. From the given system of ordinary differential equations an integro-differential equation is singled-out with respect to the plate deflection w that, together with the Dirichlet boundary conditions, makes up a boundary value problem. After finding w, other plate displacement characteristics u and ψ are defined. To approximate the problem solution for w, the Galerkin method is used. It leads to a nonlinear system of algebraic equations that is solved by the iteration method. The convergence of the iteration process is established and the error estimates are obtained for the displacement characteristics under some natural conditions. All constants from these conditions and the inequalities for the error are expressed explicitly through the initial data of the problem. The numerical examples illustrating the convergence conditions are given.

  6. Comment

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Comment
    8. Annual Index
    1. Comments on M. Miclavčič and C. Y. Wang, Completely passive natural convection, ZAMM 91/7, 601–606 (2011) (pages 1002–1004)

      W. Schneider

      Version of Record online: 8 NOV 2011 | DOI: 10.1002/zamm.201100127

      The present writer should like to make some comments on the above-mentioned paper by Miclavčič & Wang.

  7. Annual Index

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    7. Comment
    8. Annual Index
    1. Annual Index (pages 1005–1008)

      Version of Record online: 8 NOV 2011 | DOI: 10.1002/zamm.201190024

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