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441.
442.
H. Bufler 《Archive of Applied Mechanics (Ingenieur Archiv)》1998,68(9):579-588
Summary The aim of this paper is (1) to develop a rational method for the analysis of an arbitrarily laminated elastic, isotropic
or transversely isotropic hollow sphere under internal and/or external pressure, (2) to solve the problem of a periodically
layered sphere consisting of many equal groups of n different thin layers. The transfer matrix method is used, and exact closed-form solutions are worked out, supplemented by
a numerical example. It turns out that by means of the proposed homogenization an originally (periodically) inhomogeneous
isotropic sphere is replaced by a homogeneous anisotropic one belonging to the type of spherical symmetric anisotropy.
Received 20 October 1997; accepted for publication 15 December 1997 相似文献
443.
The macroscopic model governing coupled electro-chemo-mechanical phenomena in expansive clays is revisited within a rigorous
homogenization procedure applied to the microscopic governing equations which describe the local interaction between charged
clay particles and a binary monovalent aqueous electrolyte solution. The up-scaling of the microscopic electro-hydro-dynamics
leads to a two-scale approach wherein the macroscopic model appears governed by a fully coupled form of Onsager’s reciprocity
relations, mass conservation equations and a modified Terzaghi’s effective stress principle. In addition, the two-scale approach
provides microscopic representations for the effective coefficients which are exploited herein to obtain further insight in
the constitutive behavior of the electrochemical parameters and the swelling pressure. Among other effects, we show that these
microscopic closure relations are mainly dictated by the spatial variability of a microscale electric potential which satisfies
a local version of the Poisson–Boltzmann problem in a periodic unit cell, The proposed framework allows to address various
relevant still open issues regarding the constitutive behavior of swelling systems, Among them we give particular emphasis
on the analysis of the influence of the fluctuation and distortion of the electrical double layer upon the magnitude of the
electrochemical coefficients and the precise local conditions for the validity of the symmetry of Onsager’s relations. 相似文献
444.
445.
Ali Sili 《Mathematical Methods in the Applied Sciences》2002,25(4):263-288
This paper is the second of the two announced in our Note (Sili A, [16]). It generalizes to the linearized system of elasticity the results of our previous work (Sili, 2000 [15]) on the heat equation. We study the asymptotic analysis, as ? tends to zero, of the solution u? of the linearized system of elasticity posed on a composite elastic cylindrical domain Ω? with radius ? and height L. The heterogeneities of the material are assumed to be periodic with a period ? along the cylinder axis and with a period ?2 along the sections of the cylinder. It is shown that the limit problem is a system in which appear two entities: the first one (u, v, w) corresponds to the reduction of dimension 3d–1d while the second one (û, v?, ?) takes into account the homogenization process. Moreover, a corrector result is given. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
446.
Niklas Wellander 《Applications of Mathematics》2002,47(3):255-283
The Maxwell equations with uniformly monotone nonlinear electric conductivity in a heterogeneous medium, which may be non-periodic, are homogenized by two-scale convergence. We introduce a new set of function spaces appropriate for the nonlinear Maxwell system. New compactness results, of two-scale type, are proved for these function spaces. We prove existence of a unique solution for the heterogeneous system as well as for the homogenized system. We also prove that the solutions of the heterogeneous system converge weakly to the solution of the homogenized system. Furthermore, we prove corrector results, important for numerical implementations. 相似文献
447.
Joseph G. Conlon 《Transactions of the American Mathematical Society》2004,356(10):4085-4142
This paper is concerned with linear parabolic partial differential equations in divergence form and their discrete analogues. It is assumed that the coefficients of the equation are stationary random variables, random in both space and time. The Green's functions for the equations are then random variables. Regularity properties for expectation values of Green's functions are obtained. In particular, it is shown that the expectation value is a continuously differentiable function in the space variable whose derivatives are bounded by the corresponding derivatives of the Green's function for the heat equation. Similar results are obtained for the related finite difference equations. This paper generalises results of a previous paper which considered the case when the coefficients are constant in time but random in space.
448.
449.
We consider the divergent elliptic equations whose weight function and its inverse are assumed locally integrable. The equations of this type exhibit the Lavrentiev phenomenon, the nonuniqueness of weak solutions, as well as other surprising consequences. We classify the weak solutions of degenerate elliptic equations and show the attainability of the so-called W-solutions. Investigating the homogenization of arbitrary attainable solutions, we find their different asymptotic behavior. Under the assumption of the higher integrability of the weight function we estimate the difference between the exact solution and certain special approximations. 相似文献
450.
Margherita Solci 《Mathematical Methods in the Applied Sciences》2012,35(5):598-620
In this paper, we study a homogenization problem for perimeter energies in highly contrasted media; the analysis of the previous paper is carried out by removing the hypothesis that the perforated medium Rn ? E is composed of disjoint compact components. Assuming E to be the union of a finite number N of connected components E1, … ,EN, the Γ‐limit F is a multiphase energy with a ‘decoupled’ surface part, obtained by homogenization from the surface tensions in each E j, a trivial bulk term obtained as a weak limit, and a further interacting term between the phases, involving an asymptotic formula for a family minimum problems on invading an asymptotic formula for a family of minimum problems on invading domains with prescribed boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献