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1.
The relation between J-integral near model I crack tip in the orthotropic plate and displacement derivative is derived in
this paper. Meanwhile, the relation between stress intensity factor K
I
and displacement is also given in this paper. With sticking film moire interferometry method, the three-point bending beam
is tested, thus the values of J-integral and K
I
can be obtained from the displacement field, and then the truth of relation formula between J-integral and K
I
in the orthotropic composite materials is experimentally verified. 相似文献
2.
Kyu Hyun Kyung Hyun Ahn Seung Jong Lee Masataka Sugimoto Kiyohito Koyama 《Rheologica Acta》2006,46(1):123-129
In this study, linear and branched polypropylenes (PP) were compared under medium strain amplitude oscillatory shear (usually
strain amplitude range from 10 to 100%) with Fourier-transform rheology (FT rheology). On a log–log diagram, the third relative
intensity (I
3/I
1), which is a parameter to represent nonlinearity, shows a linear relationship with the strain amplitude in the range of medium
strain amplitude. The slope of I
3/I
1 of linear PP with various molecular weight and molecular weight distribution was 2 as most constitutive equations predict,
while that of branched PP was 1.64, which is lower than that of linear PP. When the linear and branch PP were blended, the
slope of I
3/I
1 was proportional to the composition of the branch PP. Therefore, it is suggested that the degree of branching can be defined
in terms of the slope of I
3/I
1 under medium amplitude oscillatory shear. 相似文献
3.
BSTO dielectric ceramic was prepared from SrTi03 and BaTi03 powders synthesized by hydrothermal method, as well as from Bao.sSro.4TiO3 powder synthesized by conventional solid-state reaction. The former can be sintered at a relatively low temperature of 1120 ℃. Characterization by SEM showed that the grain shapes of both ceramics are cubical, though the grain size of the former is much smaller. Dielectric constants measured at 20℃ were shown to vary with frequency in the range from I kHz to 2 MHz and dc bias field, and further that the dielectric loss of the former to be less than 2 × 10^- 3 in the frequency range of 20 kHz to 1 MHz, much smaller than that of the latter sample. For the former, temperature dependence of dielectric constant is much flatter and there exists an extended phase transition diffusion covering a wide temperature range of Curie temperature To. The smaller grain size of the former depresses the dc bias electrical field dependence of dielectric constant. The tunability is 7% under a bias field of 0.6 kV/mm dc. 相似文献
4.
A. Ben-Artzi I. Gohberg M. A. Kaashoek 《Journal of Dynamics and Differential Equations》1993,5(1):1-36
A linear ordinary differential operator with bounded coefficients satisfying certain homogeneous initial conditions is shown to be invertible onL
n
2
(0, ) if and only if the underlying system of differential equations has a dichotomy. Moreover, in that case the operator is proved to be a direct sum of two infinitesimal generators ofC
0-semigroups, one of which has support on the negative half-line and the other on the positive half-line. The effect of perturbations of the initial values on the dichotomy is also described. 相似文献
5.
A modified second order viscoelastic constitutive equation is used to derive a k–l type turbulence closure to qualitatively assess the effects of elastic stresses on fully-developed channel flow. Specifically,
the second order correction to the Newtonian constitutive equation gives rise to a new term in the momentum equation involving
the time-averaged elastic shear stress and in the turbulent kinetic energy transport equation quantifying the interaction
between the fluctuating elastic stress and rate of strain tensors, denoted by P
w
, for which a closure is developed and tested. This closure is based on arguments of isotropic turbulence and equilibrium
in boundary layer flows and a priori P
w
could be either positive or negative. When P
w
is positive, it acts to reduce the production of turbulent kinetic energy and the turbulence model predictions qualitatively
agree with direct numerical simulation (DNS) results obtained for more realistic viscoelastic fluid models with memory which
exhibit drag reduction. In contrast, P
w
< 0 leads to a drag increase and numerical breakdown of the model occurs at very low values of the Deborah number, which
signifies the ratio of elastic to viscous stresses. Limitations of the turbulence model primarily stem from the inadequacy
of the k–l formulation rather than from the closure for P
w
. An alternative closure for P
w
, mimicking the viscoelastic stress work predicted by DNS using the Finitely Extensible Nonlinear Elastic-Peterlin fluid model,
which is mostly characterized by P
w
> 0 but has also a small region of negative P
w
in the buffer layer, was also successfully tested. This second model for P
w
leads to predictions of drag reduction, in spite of the enhancement of turbulence production very close to the wall, but
the equilibrium conditions in the inertial sub-layer were not strictly maintained. 相似文献
6.
Zhao Kai Associate Professor 《应用数学和力学(英文版)》2000,21(5):573-578
Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ(t)-type singular integral operators in
L
B
p
(R
n), (1≤p<+∞) and H
B
1
(R
n) spaces are discussed.
Foundation item: the Education Commission of Shandong Province (J98P51)
Biography: Zhao Kai (1960-) 相似文献
7.
This paper describes a practical method for finding the invariant orbits in J
2 relative dynamics. Working with the Hamiltonian model of the relative motion including the J
2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended
to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space,
which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by
its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the
ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility
between J
2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible
configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo
simulation.
The project supported by the Innovation Foundation of Beihang University for Ph.D. Graduates, and the National Natural Science
Foundation of China (60535010). 相似文献
8.
The stability of the laminar helical flow of pseudoplastic liquids has been investigated with an indirect method consisting in the measurement of the rate of mass transfer at the surface of the inner rotating cylinder. The experiments have been carried out for different values of the geometric parameter = R
1/R
2 (the radius ratio) in the range of small values of the Reynolds number,Re < 200. Water solutions of CMC and MC have been used as pseudoplastic liquids obeying the power law model. The results have been correlated with the Taylor and Reynolds numbers defined with the aid of the mean viscosity value. The stability limit of the Couette flow is described by a functional dependence of the modified critical Taylor number (including geometric factor) on the flow indexn. This dependence, general for pseudoplastic liquids obeying the power law model, is close to the previous theoretical predictions and displays destabilizing influence of pseudoplasticity on the rotational motion. Beyond the initial range of the Reynolds numbers values (Re>20), the stability of the helical flow is not affected considerably by the pseudoplastic properties of liquids. In the range of the monotonic stabilization of the helical flow the stability limit is described by a general dependence of the modified Taylor number on the Reynolds number. The dependence is general for pseudoplastic as well as Newtonian liquids.Nomenclature
C
i
concentration of reaction ions, kmol/m3
-
d = R
2 –R
1
gap width, m
-
F
M
()
Meksyn's geometric factor (Eq. (1))
-
F
0
Faraday constant, C/kmol
-
i
l
density of limit current, A/m3
-
k
c
mass transfer coefficient, m/s
-
n
flow index
-
R
1,R
2
inner, outer radius of the gap, m
-
Re = V
m
·2d·/µ
m
Reynolds number
-
Ta
c
=
c
·d3/2·R
1
1/2
·/µ
m
Taylor number
-
Z
i
number of electrons involved in electrochemical reaction
-
= R
1/R
2
radius ratio
-
µ
apparent viscosity (local), Ns/m2
-
µ
m
mean apparent viscosity value (Eq. (3)), Ns/m2
-
µ
i
apparent viscosity value at a surface of the inner cylinder, Ns/m2
-
density, kg/m3
-
c
angular velocity of the inner cylinder (critical value), 1/s 相似文献
9.
This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show effectiveness of the obtained result. 相似文献
10.
The stability of the Couette flow of the liquid with the power law viscosity in a wide annular gap has been investigated theoretically in this work with the aid of the method of small disturbances. The Taylor number, being a criterion of the stability, has been defined using the mean apparent viscosity value in the main flow. In the whole range of the radius ratio, R
i
/R
o
and the flow index, n, considered (R
i
/R
o
0.5, n = 0.25–1.75 ), the critical value of the Taylor number Ta
c
is an increasing function of the flow index, i.e., shear thinning has destabilizing influence on the rotational flow, and dilatancy exhibits an opposite tendency.In the wide ranges of the flow index, n > 0.5, and the radius ratio, R
i
/R
o
> 0.5, the wide-gap effect on the stability limit is predicted to be almost the same for non-Newtonian fluids as for Newtonian ones. The ratio on the critical Taylor numbers for non-Newtonian and Newtonian fluids: Ta
c
(n) and Ta
c
(n = 1) obey a generalized functional dependence: Ta
c
(n)/Ta
c
(n = 1) = g(n), where g(n) is a function corresponding to the solution for the narrow gap approximation.Theoretical predictions have been compared with experimental results for pseudoplastic liquids. In the range of the radius ratio R
i
/R
o
> 0.6 the theoretical stability limit is in good agreement with the experiments, however, for R
i
/R
o
< 0.6, the critical Taylor number is considerably lower than predicted by theory. 相似文献
11.
Anisotropy of Seismic Attenuation in Fractured Media: Theory and Ultrasonic Experiment 总被引:1,自引:0,他引:1
This is a study on anisotropy of seismic attenuation in a transversely isotropic (TI) model, which is a long-wavelength equivalent
of an isotropic medium with embedded parallel fractures. The model is based on Schoenberg’s linear-slip theory. Attenuation
is introduced by means of a complex-valued stiffness matrix, which includes complex-valued normal and tangential weaknesses.
To study the peculiarities of seismic attenuation versus wave-propagation direction in TI media, numerical modeling was performed.
The model-input data were the complex-valued weaknesses found from the laboratory ultrasonic experiment made with a Plexiglas
plate-stack model, oil-saturated (wet) and air-filled (dry). The laboratory experiment and the numerical modeling have shown
that in the vicinity of the symmetry axis, in the wet model, P-wave attenuation is close to S-wave attenuation, while in the
dry model, P-wave attenuation is much greater than S-wave attenuation. Moreover, the fluid fill affects the P-wave attenuation
pattern. In the dry (air-saturated) model, the attenuation pattern in the vicinity of the symmetry axis exhibits steeper slope
and curvature than in the wet (oil-saturated) model. To define the slope or the curvature, a QVO gradient was introduced,
which was found to be proportional to the symmetry-axis Q
S/Q
P-ratio, which explains the differences between dry and wet models. Thus, depending on the Q
S/Q
P-ratio, the QVO gradient can serve as an indicator of the type of fluid in fractures, because the QVO gradient is greater
in gas-saturated than in liquid-saturated rocks. The analysis of P-wave attenuation anisotropy in seismic reflection and vertical
seismic profiling data can be useful in seismic exploration for distinguishing gas from water in fractures. 相似文献
12.
In this paper, the classical solution of the opening mode crack in the 90° layer of 0/90/0 laminates has been determined by
means of Fourier transformations and the procedure of Copson for a pair of dual integral equations. The fracture behavior
and the in situ transverse strength of the 90° layer have been quantitatively studied in graphite/epoxy laminates, based on
the solution obtained above.
The results show that the stress intensity factor of this kind of laminates, which is different from that of a single unidirectional
90° layer, decreases with the increase in thicknessb, or modulusE
L orG
LT of the 0° layer and also decreases with the decrease in the thickness of the 90° layer. So the lamination effect manifests
itself and thein situ transverse strength of the 90° layer is thereby enchanced. The theoretical calculations agree with the experimental data
presented by D.L. Flaggs.
Supported by National Natural Science Fundation of China. 相似文献
13.
F.W. Wu R.N. Ibrahim R. Das R.K. Singh Raman 《Theoretical and Applied Fracture Mechanics》2009,52(1):50-54
Many approaches for estimating mode I fracture toughness (KIC) using circumferentially notched tensile (CNT) specimen have been demonstrated in the literature. In this paper, an effective approach for estimating fracture toughness from the numerical solution of critical crack tip opening displacement (CTOD) is proposed. An elasto-plastic finite element analysis is used to estimate critical CTOD values for CNT specimens. A number of materials are analysed, and the relationship between KIC and critical CTOD for CNT specimens is obtained. The proposed relationship is validated by comparing the fracture toughness values obtained from the relationship with those obtained experimentally using CNT specimens. The fracture toughness (KIC) calculated according to this relationship from numerically obtained critical CTOD is found to be in close agreement with the experimentally obtained fracture toughness for the respective materials. 相似文献
14.
Prof. A. Siginer 《Rheologica Acta》1991,30(2):159-174
The flow of a viscoelastic liquid driven by the steadily rotating bottom cover of a cylindrical cup is investigated. The flow field and the shape of the free surface are determined at the lowest significant orders of the regular domain perturbation in terms of the angular velocity of the bottom cap. The meridional field superposed on a primary azimuthal field shows a structure of multiple cells. The velocity field and the shape of the free surface are strongly effected by the cylinder aspect ratio and the elasticity of the liquid. The use of this flow configuration as a free surface rheometer to determine the first two Rivlin-Ericksen constants is shown to be promising.Nomenclature
R, ,Z
Coordinates in the physical domain D
- , ,
Coordinates in the rest stateD
0
-
r, ,z
Dimensionless coordinates in the rest stateD
0
-
Angular velocity
-
Zero shear viscosity
-
Surface tension coefficient
-
Density
-
Dimensionless surface tension parameter
- 1, 2
The first two Rivlin-Ericksen constants
-
Stream function
-
Dimensionless second order meridional stream function
- *
Dimensionless second normal stress function
- 2
Dimensionless sum of the first and second normal stress functions
-
N
1,N
2
The first and second normal stress functions
-
n
Unit normal vector
-
D
Stretching tensor
-
A
n
nth order Rivlin-Ericksen tensor
-
S
Extra-stress
-
u
Velocity field
-
U
Dimensionless second order meridional velocity field
-
V
Dimensionless first order azimuthal velocity field
-
p
Pressure
-
Modified pressure field
-
P
Dimensionless second order pressure field
-
J
Mean curvature
-
a
Cylinder radius
-
d
Liquid depth at rest
-
D
Dimensionless liquid depth at rest
-
h
Free surface height
-
H
Dimensionless free surface height at the second order 相似文献
15.
DOUBLEHIGHORDERS-BREAKINGBIFURCATIONPOINTSANDTHEIRNUMERICALDETERMINATION¥(杨忠华,叶瑞松)YangZhonghua;(DepartmentofMathematics,Shangh... 相似文献
16.
By using the Z
p
geometrical index theory, some sufficient conditions on the multiplicity results of periodic solutions to the second-order difference equations
are obtained. By two examples, we show that our results are the best possible in the sense that the lower bound of the number of periodic solutions cannot be improved. 相似文献
17.
丁协平 《应用数学和力学(英文版)》2007,28(12):1569-1579
This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems
involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized
vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces.
Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406) 相似文献
18.
Based on shear lag model of interface between fiber and matrix, a new formula that relates the crack opening displacement
and bridging force in fibrous monolithic ceramics was constructed under the framework of small scale bridging. This formula
was applied to predict the fracture resistance orR-curve response of a three-point bending specimen made of fibrous monolithic ceramics. A parametric investigation on the influences
of fiber volume fraction, fiber radius, characteristics of constituents, BN's fracture toughness and specimen's geometry on
the bridging forces and fracture resistance in Si3N4/BN composite was carried out. The upper and lower limits of theR-curve of Si3N4/BN in small scale bridging were derived. This research revealed the role played by the above parameters in the fracture toughness
of fibrous monolithic ceramics.
Supported by National Natural Science Foundation of China (59632090). 相似文献
19.
T. Kiljański 《Rheologica Acta》1989,28(1):61-64
A simple method for correction of the wall-slip effect in a Couette rheometer was derived. The method requires only two series of measurements (two flow curves) performed in two measuring sets of any dimensions, and therefore it may be applied for the results obtained in each rheometer with a standard cup and bob set. The method was checked for experimental data and also verified theoretically for a hypothetical liquid.
H
height of cylinder
-
M
torque
-
r
distance from axis
-
R
i
,R
0
radius of inner and outer cylinder
-
R
m
average radius defined by Eq. (7)
-
u
slip velocity
-
shear rate
-
shear rate for no-slip conditions
-
Newtonian viscosity
-
angular speed
-
angular speed of the rotating cylinder 相似文献
20.
Fu Yongqing Gu Yanwei Jing Xiaotian Margam Chandrasekaran 《Acta Mechanica Solida Sinica》1997,10(1):76-85
Finite element method (FEM) has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode- II loading. The results show that: under mode- II loading, the direction of the maximum tensile stress and that of the maximum tri-axial levels (R
o
) exist at an angle of –75. 3° from the original crack plane; the maximum shear stress andR
o
= 0 exist along the original crack plane.Mode- II loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode, opening mode (or tensile mode) and sliding mode (or shear mode). A decrease in temperature causes the fracture mode to change from shear mode to tensile mode. For BHW-35 steel, this critical temperature is about –90 C. Actually, under any kind of loading mode (mode I . mode II , mode III or mixed mode), there always exist several kinds of potenital fracture modes (for example, opening mode, sliding mode, tearing mode or mixed mode). The effect of temperature under mode- II loading is actually related to the change of the elastic-plastic properties of the material. 相似文献