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1.
In this paper, we consider a materially uniform but inhomogeneous body and we are interested in three particular cases of
inhomogeneities corresponding to three distinct distributions of dislocations. The field of defects enters the equilibrium
equations through the components of the tensor field describing the relaxation procedure. We examine what form should these
components take in order for the material to admit states of anti-plane shear. The results obtained in this paper hold for
a class of materials that obey a specific form for the stored energy function. In the special case of no dislocations, this
class falls under the well known class of Neo-Hookean materials.
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2.
刘慈群 《应用数学和力学(英文版)》1981,(4)
This paper obtains the exact solution for the unsteady radial flow equations of the slightly compressible liquid through a medium with triple-poro-sity by using,the method of decomposition.This solution not only reveals the essential characters of the unsteady flow of liquid through a medium with multiple-porosity,but also comprises the existing primal results. 相似文献
3.
The interior transmission problem (ITP), which plays a fundamental role in inverse scattering theories involving penetrable
defects, is investigated within the framework of mechanical waves scattered by piecewise-homogeneous, elastic or viscoelastic
obstacles in a likewise heterogeneous background solid. For generality, the obstacle is allowed to be multiply connected,
having both penetrable components (inclusions) and impenetrable parts (cavities). A variational formulation is employed to
establish sufficient conditions for the existence and uniqueness of a solution to the ITP, provided that the excitation frequency does not belong
to (at most) countable spectrum of transmission eigenvalues. The featured sufficient conditions, expressed in terms of the
mass density and elasticity parameters of the problem, represent an advancement over earlier works on the subject in that
(i) they pose a precise, previously unavailable provision for the well-posedness of the ITP in situations when both the obstacle
and the background solid are heterogeneous, and (ii) they are dimensionally consistent, i.e., invariant under the choice of
physical units. For the case of a viscoelastic scatterer in an elastic solid it is further shown, consistent with earlier
studies in acoustics, electromagnetism, and elasticity that the uniqueness of a solution to the ITP is maintained irrespective
of the vibration frequency. When applied to the situation where both the scatterer and the background medium are viscoelastic, i.e., dissipative, on the other hand, the same type of analysis
shows that the analogous claim of uniqueness does not hold. Physically, such anomalous behavior of the “viscoelastic-viscoelastic”
case (that has eluded previous studies) has its origins in a lesser known fact that the homogeneous ITP is not mechanically
insulated from its surroundings—a feature that is particularly cloaked in situations when either the background medium or
the scatterer are dissipative. A set of numerical results, computed for ITP configurations that meet the sufficient conditions
for the existence of a solution, is included to illustrate the problem. Consistent with the preceding analysis, the results
indicate that the set of transmission values is indeed empty in the “elastic-viscoelastic” case, and countable for “elastic-elastic”
and “viscoelastic-viscoelastic” configurations. 相似文献
4.
. We consider the problem of finding a holomorphic function in a strip with a cut ${\cal A}= \{(x,y) : \, x\in\RE,\,\,0 satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the class of sectionally holomorphic functions in ?, vanishing for $|x|\to\infty. We consider the problem of finding a holomorphic function in a strip with a cut satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the
class of sectionally holomorphic functions in ?, vanishing for . A special solution can be selected by fixing the value of the circulation around the cut. The problem is obtained by linearization
of the equations of the wave‐resistance problem for a “slender” cylinder submerged in a heavy fluid and moving at uniform
speed in the direction orthogonal to its generators. The results obtained, besides their own interest, are a crucial step
for the resolution of the non‐linear problem.
(Accepted October 14, 1998) 相似文献
5.
. We study the problem of wave resistance for a “slender” cylinder submerged in a heavy fluid of finite depth with the cylinder
moving at uniform supercritical speed in the direction orthogonal to its generators. We look for a divergence‐free, irrotational
flow; the boundary of the region occupied by the fluid (consisting of the free surface, the bottom and the obstacle profile)
is assumed to belong to streamlines and the Bernoulli condition is taken on the free surface. The problem is transformed,
via the hodograph map, into a problem set in a strip with a cut. By using a “hard” version of the inverse function theorem
and by taking account of the results obtained in Part I (which we recall here), we prove the existence of a complex velocity
function satisfying all the requirements of the problem. In particular, this function is continuous up to the surface of the
obstacle, and the only possible singularities appear at the end‐points where the boundary is not smooth. Moreover, two stagnation
points appear near to the extremities of the submerged body.
(Accepted October 14, 1998) 相似文献
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7.
Jiří Neustupa 《Archive for Rational Mechanics and Analysis》2014,214(2):525-544
We formulate a new criterion for regularity of a suitable weak solution v to the Navier–Stokes equations at the space-time point (x 0, t 0). The criterion imposes a Serrin-type integrability condition on v only in a backward neighbourhood of (x 0, t 0), intersected with the exterior of a certain space-time paraboloid with vertex at point (x 0, t 0). We make no special assumptions on the solution in the interior of the paraboloid. 相似文献
8.
Transport in Porous Media - A general analytical solution procedure for the Brinkman–Forchheimer-extended Darcy model has been proposed to obtain local thermal non-equilibrium solutions for... 相似文献
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Transport in Porous Media - 相似文献