L.P. Castro  D. Kapanadze  E. Pesetskaya 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2015,95(9):952-965

We consider a steady‐state heat conduction problem in 2D unbounded doubly periodic composite materials with temperature independent conductivities of their components. Imperfect contact conditions are assumed on the boundaries between the matrix and inclusions. By introducing complex potentials, the corresponding boundary value problem for the Laplace equation is transformed into a special R‐linear boundary value problem for doubly periodic analytic functions. The method of functional equations is used for obtaining a solution. Thus, the R‐linear boundary value problem is transformed into a system of functional equations which is analysed afterwards. A new improved algorithm for solving this system is proposed. It allows to compute the average property and reconstruct the temperature and the flux at an arbitrary point of the composite. Computational examples are presented.  相似文献   

    

G. Monegato  A. Strozzi 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2005,85(7):460-470

A static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and bilaterally supported along a single periphery arc, the remaining part of the boundary being free. The contact reaction is assumed to be formed by a distributed reaction force accompanied by a distributed moment with radial axis. This plate problem is formulated in terms of an integral equation of the Prandtl type, supplemented by a vertical and a rotational equilibrium condition. It is shown that the Prandtl equation coupled to the equilibrium condition possesses a unique solution in a proper scale of weighted Sobolev‐type spaces, with certain smoothness properties, and that no solution exists if the distributed moment is absent. Finally, the behaviour of the solution at the endpoints of the support is clarified.  相似文献   

    

Laura De Lorenzis  Peter Wriggers  Thomas J.R. Hughes 《GAMM-Mitteilungen》2014,37(1):85-123

  相似文献   

    

L. Freddi  R. Paroni  T. Roubí ek  C. Zanini 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2011,91(11):845-865

A quasistatic rate‐independent brittle delamination problem and also an adhesive unilateral contact problem is considered on a prescribed normally‐positioned surface in a plate with a finite thickness. By letting the thickness of the plate go to zero, two quasistatic rate‐independent crack models with prescribed path for Kirchhoff‐Love plates are obtained as limit of these quasistatic processes.  相似文献   

    

Tsang‐Jen Hsieh  Ching‐Hua Wang  Jaw‐Yen Yang 《国际流体数值方法杂志》2008,58(9):1017-1039

Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

    

ZHAO Jia-xi  QI Hui  SU Sheng-wei 《应用数学和力学(英文版)》2008,29(6)

Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated.The solution of dynamic stress concentration factor is given using the Gteen's function and the method of complex variable functions.First,the space is divided into upper and lower parts along the interface.In the lower half space,a suitable Green's function for the problem is constructed.It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface.Thus,the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces.Also,the expressions of displacement and stress fields are obtained in this situation.Finally,examples and results of dynamic stress concentration factor are given.Influences of the cylindrical inclusion and the difierence parameters of the two mediators are discussed.  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   

    

F. Schmid 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2009,89(5):383-398

A quasi-static contact problem is considered for a nonlinear elastic system with finitely many degrees of freedom. The friction law of Coulomb is used to model friction and the friction coefficient may be anisotropic and may vary along the surface of the rigid obstacle. Existence is established following a time-incremental minimization problem. Friction is artificially decreased to resolve the discontinuity arising from making and losing contact.  相似文献   

    

Y. Lijun 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2004,84(8):528-538

The generalized Lyapunov‐Schmidt reduction is thoroughly investigated in this paper. Some new and known properties of the reduction are presented transparently. Among others we obtain two main results, an alternative proof of the equivalence of the generalized reduction and an approximation relation between the generalized Lyapunov‐Schmidt reduction and the center manifold reduction.  相似文献   

    

《Journal of the mechanics and physics of solids》2015

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order −1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.  相似文献