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

Cover image for Vol. 92 Issue 11‐12

November 2012

Volume 92, Issue 11-12

Pages 849–958

  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
    9. Annual Index
    1. You have free access to this content
      Cover Picture: ZAMM 11–12 / 2012

      Version of Record online: 5 NOV 2012 | DOI: 10.1002/zamm.201290023

  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
    9. Annual Index
    1. You have free access to this content
      Issue Information: ZAMM 11–12 / 2012

      Version of Record online: 5 NOV 2012 | DOI: 10.1002/zamm.201290024

  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
    9. Annual Index
    1. You have free access to this content
      Contents: ZAMM 11–12 / 2012 (pages 849–851)

      Version of Record online: 5 NOV 2012 | DOI: 10.1002/zamm.201209211

  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
    9. Annual Index
    1. You have free access to this content
      Comparing sampling strategies for aerodynamic Kriging surrogate models (pages 852–868)

      B. Rosenbaum and V. Schulz

      Version of Record online: 5 JUL 2012 | DOI: 10.1002/zamm.201100112

      Thumbnail image of graphical abstract

      In aerodynamic applications often evaluations of an expensive computer simulation like a CFD solver are needed for a whole range of input parameters. Dense computations to describe the global behavior of an objective function are out of reach due to limited computational resources. Surrogate models like the Kriging method allow an interpolation of collected data and a global approximation. Adaptive sampling strategies can reduce the number of required samples for accurate and efficient surrogate models by automatically identifying critical or too coarse sampled regions of the input domain. The authors compare different existing sampling strategies as well as new theoretical methods using a dense set of validation data in order to gain a deeper understanding of optimal sample distributions and lower error boundaries.

  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
    9. Annual Index
    1. A multi-time stepping integration method for the ultrasound heating problem (pages 869–881)

      I. Shevchenko, M. Kaltenbacher and B. Wohlmuth

      Version of Record online: 5 JUL 2012 | DOI: 10.1002/zamm.201200023

      Thumbnail image of graphical abstract

      A two-dimensional thermo-acoustic problem consisting of the Pennes bioheat transfer model and a nonlinear wave equation with a temperature dependent speed of sound is considered. The large discrepancy in time scales of the wave propagation and the heat conduction processes requires a multi-time stepping method allowing to solve both equations on different time scales. The authors propose a multi-time stepping scheme based on a fixed-point approach resulting in a thermo-acoustic coupling controlled by a stopping criterion. The use of a Lagrange multiplier based technique allows to efficiently incorporate the second order Engquist–Majda ABC into the weak formulation of the original problem.

    2. Closed form solution for an annular elliptic crack around an elliptic rigid inclusion in an infinite solid (pages 882–887)

      B.M. Singh, J.G. Rokne and R.S. Dhaliwal

      Version of Record online: 5 JUL 2012 | DOI: 10.1002/zamm.201100134

      The authors consider the problem of indentation of an elliptic crack by a rigid elliptic inclusion in anti-plane shear mode. Making use of integral transforms the solution of the problem is reduced into triple integral equations with cosine kernels and weight functions. Closed form solution of the triple integral equations is obtained and also closed form expressions are obtained for the displacement component and the stress intensity factor.

    3. A model for the evolution of laminates in finite-strain elastoplasticity (pages 888–909)

      K. Hackl, S. Heinz and A. Mielke

      Version of Record online: 27 JUN 2012 | DOI: 10.1002/zamm.201100155

      The authors study the time evolution in elastoplasticity within the rate-independent framework of generalized standard materials. Their particular interest is the formation and the evolution of microstructure. Providing models where existence proofs are possible is a challenging task since the presence of microstructure comes along with a lack of convexity and, hence, compactness arguments cannot be applied to prove the existence of solutions. In order to overcome this problem, they will incorporate information on the microstructure into the internal variable, which is still compatible with generalized standard materials. More precisely, they hall allow for such microstructure that is given by simple or sequential laminates. The authors will consider a model for the evolution of these laminates and will prove a theorem on the existence of solutions to any finite sequence of time-incremental minimization problems. In order to illustrate the mechanical consequences of the theory developed some numerical results, especially dealing with the rotation of laminates, are presented.

  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
    9. Annual Index
  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
    9. Annual Index
    1. On the use of sampling surfaces method for solution of 3D elasticity problems for thick shells (pages 910–920)

      G.M. Kulikov and S.V. Plotnikova

      Version of Record online: 5 JUL 2012 | DOI: 10.1002/zamm.201200028

      Thumbnail image of graphical abstract

      This paper presents a simple and effective method of solving the 3D elasticity problems for thick shells. It is based on the new concept of sampling surfaces (S-surfaces) inside the shell body. According to this concept, we introduce N not equally located S-surfaces parallel to the midsurface and choose displacements of these surfaces as basic shell unknowns. Such choice allows one to represent the governing equations of the proposed higher order shell model in a very compact form and to solve the 3D static problems for thick plates and shells efficiently.

    2. Modeling the saturation process of flows through rigid porous media by the solution of a nonlinear hyperbolic system with one constrained unknown (pages 921–936)

      R.M. Saldanha da Gama, J.J. Pedrosa Filho and M.L. Martins-Costa

      Version of Record online: 27 JUN 2012 | DOI: 10.1002/zamm.201100031

      This work proposes a mathematical model to study the filling up of an unsaturated rigid porous medium by a liquid identifying the transition from unsaturated to saturated flow. The mechanical model employs a mixture theory approach – in which the mixture consists of three overlapping continuous constituents, representing the porous matrix (solid constituent), the incompressible fluid (liquid constituent) and an inert gas constituent included to account for its compressibility. The mathematical description gives rise to a nonlinear hyperbolic system in which the fluid fraction must satisfy an inequality – an upper bound – in order to be physically realistic. The model introduced in this work accounts for the physical upper bound of the fluid fraction (and the saturation) that depends on the volume of the pores. The complete solution of a Riemann problem associated to the system of conservation laws satisfying the constraint given by the saturation upper bound is presented.

    3. Elastic buckling of axisymmetric cylindrical shells under axial load using first order shear deformation theory (pages 937–944)

      F. Mahboubi Nasrekani and H.R. Eipakchi

      Version of Record online: 13 JUL 2012 | DOI: 10.1002/zamm.201200004

      Thumbnail image of graphical abstract

      The elastic buckling stress of axisymmetric cylindrical shells under uniform axial load is determined analytically by using the first order shear deformation theory. The equilibrium equations are derived by the virtual work principle and then the stability equations are extracted from them. They are systems of differential equations, which are solved analytically by using the perturbation method. The effects of the geometrical properties on the buckling stress are investigated by a parametric study. The results are compared with the finite elements methods.

    4. Numerical investigation of 1D continuum dynamical models of discrete chain (pages 945–954)

      I.V. Andrianov, G.A. Starushenko and D. Weichert

      Version of Record online: 14 AUG 2012 | DOI: 10.1002/zamm.201200057

      This paper is devoted to the numerical analysis of the various continuum models of a 1D discrete media. The authors consider the solution in the form of a traveling wave caused by the initial perturbation. The solution is obtained by Fourier transformation inverted numerically. Then they compare solutions of discrete and continuum models for wave velocity. Numerical calculations show that all the above described nonlocal theories qualitatively equally well describe the propagation of waves in a discrete media. The advantage of improved quasi-continuum approximation is manifested in those cases where you need to describe the high modes of oscillation of the discrete finite chain.

  8. Annual Index

    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
    9. Annual Index
    1. Annual Index (pages 955–958)

      Version of Record online: 5 NOV 2012 | DOI: 10.1002/zamm.201290026

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