B.X. Xu  M.Z. Wang 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2007,87(1):59-69

Eshelby proved in 1957 that the strain field within a homogeneous ellipsoidal inclusion embedded in an infinite isotropic media is uniform, when the eigenstrain prescribed in the inclusion is uniform. This uniform strain field property was conjectured to hold exclusively for the ellipsoidally shaped inclusions. In recent studies the authors have discovered the arithmetic mean properties of the strains for N‐fold (N is greater than 2 but unequal to 4) rotational symmetrical inclusions with uniform eigenstrains, called the arithmetic mean theorem of the Eshelby tensors. In this paper, we investigate the two‐dimensional rotational symmetrical inclusions with rotational symmetrical eigenstrains. It is shown that for N‐fold (N is greater than 4) rotational symmetrical inclusions with the same fold rotational symmetrical eigenstrains which are constant on the boundary of the inclusion, the arithmetic mean of the strains at N rotational symmetrical points presents special properties: For the points outside the inclusion, the arithmetic mean vanishes; for the points inside the inclusion, the arithmetic mean is in direct proportion to the eigenstrain on the boundary of the inclusion, with the coefficient tensor equal to the Eshelby tensor for circular inclusions. It is followed that the average strain over the inclusion domain and the line average of strains along a concentric circle inside the inclusion also equal the eigenstrains on the boundary of the inclusion multiplied by the Eshelby tensor for circular inclusions. These properties obtained in this paper can be safely reduced to the results for uniform eigenstrains shown in our former works.  相似文献   

    

A. Rietz 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2007,87(4):290-302

We examine the existence of solutions to incremental friction problems for a continuous elastic object in contact with obstacles. The contact is modelled by a modified Signorini impenetrability contact condition. In particular, we consider the case when the boundary conditions of the object permit the object to perform rigid body motions. This means that the friction forces have to balance the applied forces if the object is to remain stationary. The main result is friction dependent conditions on the applied force that is sufficient for the existence of solutions to the incremental friction problem.  相似文献   

    

S. Berres  R. Bürger 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2007,87(10):665-691

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Guangwu Yan  Jianying Zhang  Yanhong Liu  Yinfeng Dong 《国际流体数值方法杂志》2007,55(1):41-56

In this paper, we propose a new lattice Boltzmann model for the compressible Navier–Stokes equations. The new model is based on a three‐energy‐level and three‐speed lattice Boltzmann equation by using a method of higher moments of the equilibrium distribution functions. As the 25‐bit model, we obtained the equilibrium distribution functions and the compressible Navier–Stokes equations with the second accuracy of the truncation errors. The numerical examples show that the model can be used to simulate the shock waves, contact discontinuities and supersonic flows around circular cylinder. The numerical results are compared with those obtained by traditional method. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

    

Eberhard Bänsch  Jordi Paul  Alfred Schmidt 《国际流体数值方法杂志》2013,71(10):1282-1296

In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

    

Z. D. Wu  L. Sun  Z. Zong 《国际流体数值方法杂志》2013,73(1):74-102

An interface‐capturing method based on mass fraction is developed to solve the Riemann problem in multi‐component compressible flow. Equations of mass fraction with modified form, which is derived from conservative equations of mass, are employed here to capture the interface. By introducing mass fraction into Euler equations system, as well as other conservative coefficients, a quasi‐conservative numerical model is created. Numerical examples show that the mass fraction model performs well not only in multi‐component fluids modeled by simple stiffened gas equation of state (EOS) but also in that modeled by complex Mie–Grüneisen EOS. Moreover, the mass fraction model is applied to Riemann problem with piecewise EOS; the expression of which depends on density. It is found that the mass fraction model can well adapt to the analytic change in piecewise EOS and produce accuracy solutions with fewer unknown quantities, and the model can be easily extended to m‐component fluid mixture by using only m + 4 equations with no additional conditions. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

    

《Mechanics Research Communications》2013

The notion of shear centre in Saint-Venant beam theory was introduced by Robert Maillart who envisaged it to explain the results of experimental tests on beams with C-shaped sections. In literature, the location of the shear centre is provided in terms of flexure functions. The new result is a formula for the shear centre, based on the knowledge of the sole twist warping function of the cross-section.  相似文献   

    

Steffen Börm  Sabine Le Borne 《国际流体数值方法杂志》2012,68(1):83-98

The (mixed finite element) discretization of the linearized Navier–Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as ‘grad‐div’ (GD) stabilization, as well as on the discrete side where it is known as an ‘augmented Lagrangian’ (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ??‐LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ??‐LU factorization in the preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

    

X. Chen  S. Akella  I. M. Navon 《国际流体数值方法杂志》2012,68(3):377-402

In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

Yuan Li  Rong An 《国际流体数值方法杂志》2012,69(3):550-566

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献