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1.
Here we investigate whether the deformation observed in an experiment in which the porcine circumflex coronary artery is subjected
to inflation at constant length included in the class,
,
,
. We find that this is not the case and discuss its implications in the study of the mechanics of this artery. Moreover, we
identify and quantify the uncertainty in the value of the invariants of the left Cauchy–Green tensor inferred from the 2D
motion of markers affixed to the surface of the test specimen, and suggest that 3D tracking of markers is needed due to inherent
bending and twisting induced by pressurization in vitro. 相似文献
2.
In this paper, a digital photoelastic system was employed to observe the stress distribution generated by an ultrasonic wave
impinged at the edge of a strip. According to the classical photoelastic theory, gray level distribution of the photoelastic
fringe patterns was formulated and expressed in the form of
, where J0 is the zeroth-order Bessel function. This new technique is called the time-averaged photoelastic method. To verify the proposed
method, the distribution of
was superimposed onto the distribution of gray level of the experimentally obtained photoelastic fringe pattern caused by
standing wave only. Except regions near the center of fringes, well-matched results were found. 相似文献
3.
K. Arakawa T. Mada H. Komatsu T. Shimizu M. Satou K. Takehara G. Etoh 《Experimental Mechanics》2006,46(6):691-697
The oblique impact between a golf ball and a rigid steel target was studied using a high-speed video camera. Video images
recorded before and after the impact were used to determine the inbound velocity v
i, rebound velocity v
r, inbound angle θi, rebound angle θr, and the coefficient of restitution e. The results showed that θr and e decreased as v
i increased. The maximum compression ratio ηc, contact time t
c, average angular velocity
, and tangential velocity
, along the target were determined from images obtained during the impact. The images demonstrated that ηc increased with v
i while t
c decreased. In addition,
and
increased almost linearly as v
i increased. A rigid body model was used to estimate the final angular velocity ω* and tangential velocity νt* at the end of the impact; these results were then compared with experimental data. 相似文献
4.
A connection between the symmetries of manifolds and differential equations is sought through the geodesic equations of maximally symmetric spaces, which have zero, constant positive or constant negative curvature. It is proved that for a space admitting so(n+1) or so(n,1) as the maximal isometry algebra, the symmetry of the geodesic equations of the space is given by so( or (where d
2 is the two-dimensional dilation algebra), while for those admitting (where represents semidirect sum) the algebra is sl(n+2). A corresponding result holds on replacing so(n) by so(p,q) with p+q = n. It is conjectured that if the isometry algebra of any underlying space of non-zero curvature is h, then the Lie symmetry algebra of the geodesic equations is given by , provided that there is no cross-section of zero curvature at the point under consideration. If there is a flat subspace of dimension m, then the symmetry group becomes ). 相似文献
5.
We show two examples of systems
in
with
such that |Zt| is strictly decreasing in time for any n but
as
. 相似文献
6.
Existence of Weak Solutions to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with Shear Rate Dependent Viscosity 总被引:1,自引:0,他引:1
Jörg Wolf 《Journal of Mathematical Fluid Mechanics》2007,9(1):104-138
In the present paper we prove the existence of weak solutions
to the equations of non-stationary motion of an incompressible fluid with shear rate dependent viscosity in a cylinder Q = Ω × (0,T), where
denotes an open set. For the power-low model with
we are able to construct a weak solution
with ∇ · u = 0. 相似文献
7.
We investigate the dynamics of the semiflow φ induced on H01(Ω) by the Cauchy problem of the semilinear parabolic equation
on Ω. Here
is a bounded smooth domain, and
has subcritical growth in u and satisfies
. In particular we are interested in the case when f is definite superlinear in u. The set
of attraction of 0 contains a decreasing family of invariant sets
distinguished by the rate of convergence
. We prove that the Wk’s are global submanifolds of
, and we find equilibria in the boundaries
. We also obtain results on nodal and comparison properties of these equilibria. In addition the paper contains a detailed exposition of the semigroup approach for semilinear equations, improving earlier results on stable manifolds and asymptotic behavior near an equilibrium.Supported by DFG Grant BA 1009/15-1. 相似文献
8.
The in-plane deformation fields near a stationary crack tip for thin, single edge-notched (SEN) specimens, made from Plexiglas, 3003 aluminum alloy and 304 stainless steel, have been successfully obtained by using computer vision. Results from the study indicate that (a) in-plane deformations ranging from elastic to fully plastic can be obtained accurately by the method, (b) for U,
and
, the size of the HRR dominant zone is much smaller than forV and
, respectively. Since these results are in agreement with recent analytical work, suggesting that higher order terms will be needed to accurately predict trends in the data, it is clear that the region where the first term in the asymptotic solution is dominant is dependent on the component of the deformation field being studied, (c) the HRR solution can be used to quantity
only in regions where theplastic strains strongly dominate the elastic strain components (i.e., when
); forV, the HRR zone appears to extend somewhat beyond this region, (d) the displacement componentU does not have the HRR singularity anywhere within the measurement region for either 3003 aluminum or 304 SS. However, the displacement componentV agrees with the HRR slope up to the plastic-zone boundary in 3003 aluminum (
) and over most of the region where measurements were obtained (
) in 304 SS and (e) the effects of end conditions must be included in any finite-element model of typical SEN specimen geometries to accurately calculate theJ integral and the crack-tip fields.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11. 相似文献
9.
We consider the motion of a generalized Newtonian fluid, where the extra stress tensor is induced by a potential with p-structure (p = 2 corresponds to the Newtonian case). We focus on the three dimensional case with periodic boundary conditions and extend the existence result for strong solutions for small times from
\tfrac{5}{3}$$
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(see [16]) to
\tfrac{7}{5}.$$
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Moreover, for
we improve the regularity of the velocity field and show that
for all
0.$$
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Within this class of regularity, we prove uniqueness for all
\tfrac{7}{5}.$$
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We generalize these results to the case when p is space and time dependent and to the system governing the flow of electrorheological fluids as long as
相似文献
10.
We consider the Cauchy problem for incompressible Navier–Stokes equations
with initial data in
, and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have
, as long as
stays finite. 相似文献
11.
A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally
graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for
a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis
coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further
insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used
to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to
conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different
specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor
(K
ID
) and crack-tip velocity (
) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar
-K
ID
relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack
propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about
10% lower than the value of local fracture toughness in FGMs. 相似文献
12.
13.
A nonlinear nonlocal model arising from synaptically coupled neuronal networks with two integral terms is considered. The existence and stability of several traveling wave solutions are established by using ideas in differential equations and functional analysis. Steady-state solutions of some inhomogeneous integral–differential equations are also investigated. We consider several types of kernel functions: (I) positive functions, such as
and
, where ρ>0 is a constant; (II) nonnegative kernels with compact supports, for examples, (i)
1$$" align="middle" border="0">
, and (ii)
{\pi\over 2}$$" align="middle" border="0">
; (III) Mexican hat type kernel functions, such as
and
, where A>B>0 and a>b>0 are constants.Dedicated to Professor Yulin Zhou and Professor Boling Guo on the Occassions of their birthdays. 相似文献
14.
Part I of this work addressed quasi-static loading of the shear compression specimen (SCS), which has been especially developed
to investigate the shear dominant response of materials at various strain rates. The stress and strain states were characterized
numerically. Approximations were presented to reduce the measured load,P, and displacement,d, into equivalent stress
and strain
. This paper addresses dynamic loading of the SCS. Several simulations were made for representative materials, whose stress-strain
behavior is assumed to be rate-independent. The results show that stress wave loading induces strong oscillations in theP-d curve. However, the
curve remains smooth in the gage section. The oscillations are about the quasistatic load values, so that with suitable filtering
of the dynamicP-d curves, the quasi-static ones are readily recovered. Consequently, the approach that was developed for quasi-static loading
of the SCS is now extended to dynamic loading situations. The average strain rate is rather constant and scales linearly with
the prescribed velocity. As the plastic modulus becomes smaller, the strain rate reaches higher values. Friction at the end
pieces of the specimen is also investigated, and shown to have a small overall influence on the determined mechanical characteristics.
This paper thereby confirms the potential of the SCS for large strain testing of materials, using a unified approach, over
a large range of strain rates in a seamless fashion. 相似文献
15.
Takayuki Kobayashi Takashi Suzuki Kazuo Watanabe 《Journal of Mathematical Fluid Mechanics》2006,8(3):382-397
This paper is concerned with the component-wise regularity of the solution to the stationary Maxwell or Stokes systems. We
assume that there is a surface
in R3, regarded as an interface, and the solution u to one of the systems is smooth except for this
. Then, under these assumptions, we can show that some components of u are smooth across
. In the Maxwell system, the normal component of u is always regular across
. On the other hand, in the Stokes system, the singularity of u across
can only arise to the normal derivatives of its tangential components. Furthermore, these results are shown to be optimal. 相似文献
16.
We introduce a new energetic formulation for the inelastic rate-independent behavior of standard generalized materials. This formulation is solely based on the classical elastic energy-storage potential
and a dissipation potential
, and it replaces the classical variational inequalities which describe the flow rules for the inelastic variables like the plastic deformation and the hardening parameters. The energetic formulation has the major advantage that it is defined for a larger class of processes since it does not involve any derivatives of the strains or the internal variables, thus allowing for an analysis of processes involving sharp interfaces, localization or microstructure. Two new quantities are derived from
and
. First, this is the global dissipation distance
on the manifold of internal states. Second, the reduced stored-energy density
contains the comprised information of the elastic and plastic material properties via minimization of
over the new internal variable. Several stability concept are derived and used to analyze failure mechanism. Finally, a natural incremental method is proposed which reduces to a minimization problem and can be solved efficiently using
.Received: 5 December 2002, Accepted: 10 February 2003, Published online: 27 June 2003PACS:
66.20.F2, 62.40.+i, 80.40.cmA. Mielke: Research partially supported by DFG within the SFB 404 Multifield Problems 相似文献
17.
Jürgen Saal 《Journal of Mathematical Fluid Mechanics》2006,8(2):211-241
We study the initial-boundary value problem for the Stokes equations with Robin boundary conditions in the half-space
It is proved that the associated Stokes operator is sectorial and admits a bounded H∞-calculus on
As an application we prove also a local existence result for the nonlinear initial value problem of the Navier–Stokes equations
with Robin boundary conditions. 相似文献
18.
The unsteady dynamics of the Stokes flows, where
, is shown to verify the vector potential–vorticity (
) correlation
, where the field
is the pressure-gradient vector potential defined by
. This correlation is analyzed for the Stokes eigenmodes,
, subjected to no-slip boundary conditions on any two-dimensional (2D) closed contour or three-dimensional (3D) surface. It is established that an asymptotic linear relationship appears, verified in the core part of the domain, between the vector potential and vorticity,
, where
is a constant offset field, possibly zero. 相似文献
19.
Dr. M. Dow Dr. H. Nakamura Prof. Dr. G. I. N. Rozvany 《Archive of Applied Mechanics (Ingenieur Archiv)》1982,52(5):335-353
Summary The first part of this paper is concerned with the optimal design of spherical cupolas obeying the von Mises yield condition. Five different load combinations, which all include selfweight, are investigated. The second part of the paper deals with the optimal quadratic meridional shape of cupolas obeying the Tresca yield condition, considering selfweight plus the weight of a non-carrying uniform cover. It is established that at long spans some non-spherical Tresca cupolas are much more economical than spherical ones.
List of Symbols ak, bk, ck, Ak, Bk, Ck coefficients used in series solutions - A, B constants in the nondimensional equation of the meridional curve - normal component of the load per unit area of the middle surface - meridional and circumferential forces per unit width - radial pressure per unit area of the middle surface, - skin weight per unit area of the middle surface, - vertical external load per unit horizontal area, - base radius, - R radius of convergence - s - cupola thickness, - u, w subsidiary functions for quadratic cupolas - vertical component of the load per unit area of middle surface - resultant vertical force on a cupola segment - structural weight of cupola, - combined weight of cupola and skin, - distance from the axis of rotation, - vertical distance from the shell apex, - z auxiliary variable in series solutions - specific weight of structural material of cupola - radius of the middle surface, - uniaxial yield stress - meridional stress, - circumferential stress, - a, b, c, d, e subsidiary variables used in evaluating the meridional stress - auxiliary function used in series solutions This paper constitutes the third part of a study of shell optimization which was initiated and planned by the late Prof. W. Prager 相似文献
Optimale Kuppeln gleicher Festigkeit: Kugelschalen und axialsymmetrische Schalen
Übersicht Im ersten Teil dieser Arbeit wird der optimale Entwurf sphärischer Kuppeln behandelt, wobei die von Misessche Fließbewegung zugrunde gelegt wird. Fünf verschiedene Lastkombinationen werden untersucht. Der zweite Teil befaßt sich mit der optimalen quadratischen Form des Meridians von Kuppeln, die der Fließbedingung von Tresca folgen.
List of Symbols ak, bk, ck, Ak, Bk, Ck coefficients used in series solutions - A, B constants in the nondimensional equation of the meridional curve - normal component of the load per unit area of the middle surface - meridional and circumferential forces per unit width - radial pressure per unit area of the middle surface, - skin weight per unit area of the middle surface, - vertical external load per unit horizontal area, - base radius, - R radius of convergence - s - cupola thickness, - u, w subsidiary functions for quadratic cupolas - vertical component of the load per unit area of middle surface - resultant vertical force on a cupola segment - structural weight of cupola, - combined weight of cupola and skin, - distance from the axis of rotation, - vertical distance from the shell apex, - z auxiliary variable in series solutions - specific weight of structural material of cupola - radius of the middle surface, - uniaxial yield stress - meridional stress, - circumferential stress, - a, b, c, d, e subsidiary variables used in evaluating the meridional stress - auxiliary function used in series solutions This paper constitutes the third part of a study of shell optimization which was initiated and planned by the late Prof. W. Prager 相似文献
20.
R. Danchin 《Journal of Mathematical Fluid Mechanics》2006,8(3):333-381
This paper is devoted to the study of the initial value problem for density dependent incompressible viscous fluids in a bounded
domain of
with
boundary. Homogeneous Dirichlet boundary conditions are prescribed on the velocity. Initial data are almost critical in term
of regularity: the initial density is in W1,q for some q > N, and the initial velocity has
fractional derivatives in Lr for some r > N and
arbitrarily small. Assuming in addition that the initial density is bounded away from 0, we prove existence and uniqueness
on a short time interval. This result is shown to be global in dimension N = 2 regardless of the size of the data, or in dimension N ≥ 3 if the initial velocity is small.
Similar qualitative results were obtained earlier in dimension N = 2, 3 by O. Ladyzhenskaya and V. Solonnikov in [18] for initial densities in W1,∞ and initial velocities in
with q > N. 相似文献