M. Wiesner  M. Kaczmarski  A. Eichner  S. Mielcarek  B. Mrz 《Crystal Research and Technology》2006,41(6):553-556

Elastic and dielectric properties of glaserite K₃Na(SO₄)₂ single crystal were examined using the method of composite oscillators, Brillouin light scattering methods and dielectric spectroscopy. Measurements were performed in the temperature range from 18 K to 300 K. Anomalies in the temperature dependencies of Brillouin shift and dielectric permittivity at about 70 K confirmed the earlier predicted phase transition at 75 ± 25 K. Temperature dependences of the resonance frequency of the vibrating composite oscillator, Brillouin shift measured in the [110] direction, components of dielectric permittivity tensor reveal an anomaly at about 50 K. Moreover, thermal hysteresis of the dielectric permittivity suggested the presence of an incommensurate state between T ₁ = 50 K and T ₂ = 70 K. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

    

D. Iean 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2005,85(5):351-365

This paper applies the technique of successive approximation to the nonlinear theory of elastic materials with voids, as developed by Nunziato and Cowin [2]. The complete set of equations for the first and second order approximation is derived. The torsion problem within the second‐order theory is studied. It is shown that the solution can be expressed in terms of solutions of some two‐dimensional problems. The theory is applied to study the torsion of a circular cylinder. It is shown that an infinitesimal twist produces a second‐order volume fraction field which is proportional to the square of the amount of torsion.  相似文献   

    

G. Teichelmann  M. Schaub  B. Simeon 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2005,85(12):864-877

Mathematical models and numerical methods for the computation of both static equilibria and dynamic oscillations of railroad catenaries are derived and analyzed. These cable systems form a complex network of string and beam elements and lead to coupled partial differential equations in space and time where constraints and corresponding Lagrange multipliers express the interaction between carrier, contact wire, and pantograph head. For computing static equlibria, three different algorithms are presented and compared, while the dynamic case is treated by a finite element method in space, combined with stabilized time integration of the resulting differential algebraic system. Simulation examples based on reference data from industry illustrate the potential of such computational tools.  相似文献   

    

Xikui Li  Xianhong Han 《国际流体数值方法杂志》2005,49(4):395-416

Stabilized fractional step algorithm has been widely employed for numerical solution of incompressible Navier–Stokes equations. However, smaller time step sizes are required to use for existing explicit and semi‐implicit versions of the algorithm due to their fully or partially explicit nature particularly for highly viscous flow problems. The purpose of this paper is to present two modified versions of the fractional step algorithm using characteristic based split and Taylor–Galerkin like based split. The proposed modified versions of the algorithm are based on introducing an iterative procedure into the algorithm and allow much larger time step sizes than those required to the preceding ones. A numerical study of stability at acceptable convergence rate and accuracy as well as capability in circumventing the restriction imposed by the LBB condition for the proposed iterative versions of the algorithm is carried out with the plane Poisseuille flow problem under different Reynolds numbers ranging from low to high viscosities. Numerical experiments in the plane Poisseuille flow and the lid‐driven cavity flow problems demonstrate the improved performance of the proposed versions of the algorithm, which are further applied to numerical simulation of the polymer injection moulding process. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

    

J. Fehr  M. Fischer  B. Haasdonk  P. Eberhard 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2013,93(8):501-519

The method of elastic multibody systems is frequently used to describe the dynamical behavior of the mechanical subsystems in multi‐physics simulations. One important issue for the simulation of elastic multibody systems is the error‐controlled reduction of the flexible body's degrees of freedom. By the use of second order frequency‐weighted Gramian matrix based reduction techniques the distribution of the loads is taken into account a‐priori and very accurate models can be obtained within a predefined frequency range and even a‐priori error bounds are available. However, the calculation of the frequency‐weighted Gramian matrices requires high computational effort. Hence, appropriate approximation schemes have to be used to find the dominant eigenspace of these matrices. In the current contribution, the matrix integral needed for calculating the Gramian matrices is approximated by quadratures using integral kernel snapshots. The number and location of these snapshots have a strong influence on the reduction results. Sophisticated snapshot selection methods based on Greedy algorithms from the reduced basis methods are used to construct the optimal location of snapshot frequencies. The method can be viewed as an automatic determination of optimal frequency weighting and as an adaptive learning of quadrature rules. One ingredient of Greedy algorithms is the need of error measures. To gain computational advantage two different error estimators are derived and used in the Greedy algorithm instead of the absolute or relative error.  相似文献   

    

W.C. Sanguinet 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2011,91(12):944-956

The equations of motion for an elastic laminar spatial‐temporal composite are investigated. It is assumed that the composite is binary, that is, it is assembled of two original constituents capable of changing (in space‐time) their material density, as well as their material stiffness. The condition of plane strain was then imposed on the composite. 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 of one dimensional strain that arises when longitudinal dynamic disturbances propagate along an elastic bar.  相似文献   

    

I. Hlav ek 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2007,87(10):747-761

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J. Frehse  M. Specovius‐Neugebauer 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2012,92(2):113-123

We consider the loading of an elastic perfectly plastic body governed by the Prandtl‐Reuss law. It is shown that the stress velocities of the body have fractional derivatives of order ‐ δ up to the boundary in the direction of the loading parameter, and of order ⅓ ‐ δ in the interior of the body in direction of the space variables.  相似文献   

    

W. Saetiew  S. Chucheepsakul 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2012,92(6):479-489

In this article, the post‐buckling behavior of a simply supported column made of nonlinear elastic materials subjected to an end axial force is investigated. The column has a uniform rectangular cross‐section in which the stress–strain relationship of such materials is represented by the generalized Ludwick constitutive law. To derive the governing equations, both geometrical and material nonlinearities have been considered. Further, a set of highly nonlinear simultaneous first‐order differential equations with boundary conditions is established and numerically solved by the shooting method. Several numerical results are carried out and discussed highlighting the significant influences of the material nonlinearity parameter n on the equilibrium configurations and the equilibrium paths. From the results, there are many interesting features associated with the nonlinear hardening column such as a non‐monotonic bifurcation curve, the limit load point, snap‐through phenomenon, and hysteresis loop. Furthermore, the numerical results are compared with previous studies in order to test the validity and accuracy of the present method.  相似文献   

    

Markus Hütter  Clarisse Luap  Hans Christian Öttinger 《Rheologica Acta》2009,48(3):301-316

The incorporation of energy elastic effects in the modeling of flowing polymeric liquids is discussed. Since conformational energetic effects are determined by structural features much smaller than the end-to-end vector of the polymer chains, commonly employed single conformation tensor models are insufficient to describe energy elastic effects. The need for a local structural variable is substantiated by studying a microscopic toy model with energetic effects in the setting of a generalized canonical ensemble. In order to examine the dynamics of flowing polymeric liquids with energy elastic effects, a thermodynamically admissible set of evolution equations is presented that accounts for the evolution of the microstructure in terms of a slow tensor, as well as a fast, local scalar variable. It is demonstrated that the temperature used in the definition of the heat flux is directly related to the Lagrange multiplier of the microscopic energy in the generalized canonical partition function. The temperature equation is discussed with respect to, first, the dependence of the heat capacity on the polymer conformation and, second, the possibility to measure experimentally the effects of the conformational energy.

Markus HütterEmail:

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