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1.
Application of differential-integral equation to elliptical crack problem under shear load 总被引:1,自引:0,他引:1
Stress intensity factors for an elliptical crack under shear loading are investigated. The differential-integral equation is applied to solve the problem. It is found that, if the integrated function takes the form of (1 − (x/a)2 − (y/b)2)1/2 xm yn, a and b being the major and minor axis of the ellipse, the relevant differential-integral equation can be evaluated. Using this property, the boundary value problems are solved for the shear loading in the form of power function. Finally, results are presented for twelve particular example problems. 相似文献
2.
Wang Zikun 《Acta Mechanica Sinica》1994,10(1):49-60
Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems
for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components
and electric potential functions are represented by a singular function satisfying some special partial differential equations
of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another
form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions
into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore,
the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed
under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The
results show that the stress and the electric displacement components near the crack tip have (r
−1/2) singularity.
The project supported by the Natural Science Foundation of Shaanxi Province, China 相似文献
3.
We find conditions for the unique solvability of the problem u
xy
(x, y) = f(x, y, u(x, y), (D
0
r
u)(x, y)), u(x, 0) = u(0, y) = 0, x ∈ [0, a], y ∈ [0, b], where (D
0
r
u)(x, y) is the mixed Riemann-Liouville derivative of order r = (r
1, r
2), 0 < r
1, r
2 < 1, in the class of functions that have the continuous derivatives u
xy
(x, y) and (D
0
r
u)(x, y). We propose a numerical method for solving this problem and prove the convergence of the method.
__________
Translated from Neliniini Kolyvannya, Vol. 8, No. 4, pp. 456–467, October–December, 2005. 相似文献
4.
Discrete dipoles located near the crack tip play an important role in nonlinear electric field induced fracture of piezoelectric
ceramics. A physico-mathematical model of dipole is constructed of two generalized concentrated piezoelectric forces with
equal density and opposite sign. The interaction between crack and electric dipole in piezoelectricity is analyzed. The closed
form solutions, including those for stress and electric displacement, crack opening displacement and electric potential, are
obtained. The function of piezoelectric anisotropic direction,p
a
(θ)=cosθ+p
a
sinθ, can be used to express the influence of a dipole's direction. In the case that a dipole locates near crack tip, the
piezoelectric stress intensity factor is a power function with −3/2 index of the distance between dipole and crack tip.
Supported by National Natural Science Foundation of China(No. 10072033) 相似文献
5.
The problem of the self-similar boundary flow of a “Darcy-Boussinesq fluid” on a vertical plate with temperature distribution
T
w(x) = T
∞+A·x
λ and lateral mass flux v
w(x) = a·x
(λ−1)/2, embedded in a saturated porous medium is revisited. For the parameter values λ = 1,−1/3 and −1/2 exact analytic solutions
are written down and the characteristics of the corresponding boundary layers are discussed as functions of the suction/ injection
parameter in detail. The results are compared with the numerical findings of previous authors.
Received on 8 March 1999 相似文献
6.
孙鸿烈 《应用数学和力学(英文版)》1999,20(7):789-794
IntroductionFrompracticalproblem,wecouldconcludemanyproblemsaboutsolvingparabolicpartialdiferentialequation.Nowtherearemanynu... 相似文献
7.
Aloisio Neves 《Journal of Dynamics and Differential Equations》2010,22(3):617-627
This paper is concerned with the spectrum the Hill operator L(y) = −y′′ + Q(x) y in L2per[0, p]{L^2_{{\rm per}}[0, \pi]}. We show that the eigenvalues of L can be characterized by knowing one of its eigenfunctions. Applications are given to nonlinear stability of a class of periodic
problems. 相似文献
8.
Yoshihisa Morita Hirokazu Ninomiya 《Journal of Dynamics and Differential Equations》2006,18(4):841-861
We deal with a reaction–diffusion equation u
t
= u
xx
+ f(u) which has two stable constant equilibria, u = 0, 1 and a monotone increasing traveling front solution u = φ(x + ct) (c > 0) connecting those equilibria. Suppose that u = a (0 < a < 1) is an unstable equilibrium and that the equation allows monotone increasing traveling front solutions u = ψ1(x + c
1
t) (c
1 < 0) and ψ2(x + c
2
t) (c
2 > 0) connecting u = 0 with u = a and u = a with u = 1, respectively. We call by an entire solution a classical solution which is defined for all
. We prove that there exists an entire solution such that for t≈ − ∞ it behaves as two fronts ψ1(x + c
1
t) and ψ2(x + c
2
t) on the left and right x-axes, respectively, while it converges to φ(x + ct) as t→∞. In addition, if c > − c
1, we show the existence of an entire solution which behaves as ψ1( − x + c
1
t) in
and φ(x + ct) in
for t≈ − ∞. 相似文献
9.
Aloisio Neves 《Journal of Dynamics and Differential Equations》2009,21(3):555-565
This paper is concerned with the spectrum the Hill operator L(y) = −y′′ + Q(x) y in L2per[0, p]{L^{2}_{\rm per}[0, \pi]} . We show that the eigenvalues of L can be characterized by knowing one of its eigenfunctions. Applications are given to nonlinear stability of a class of periodic
problems. 相似文献
10.
A unified damage and fracture model, the combinatory work density model, which is suitable for either non-cracked body or
cracked body has been suggested[t−7]. In the present paper, the deformation and fracture of the two kinds of tensile spceimen and TPB specimen made of 40Cr steel
have been simulated by using the new model together with the large elastic-plastic deformation finite element method. The
results give a good picture of the whole deformation and fracture processes of the specimens in experiments; especially, the
results on the TPB specimen can be used to obtain the relationship between load and displacement at the loading pointP-Δ, and between crack extension and displacement at the loading point Δa-Δ, the resistance curveJ
R
-Δa and the fracture toughnessJ
1C
. All the results are in remarkable agreement with those obtained by experiments. Therefore the model suggested here can be
used to simulate crack initiation and propagation in non-cracked body and fracture initiation and crack stable propagation
in cracked body.
The project supported by National Natural Science Foundation of China 相似文献
11.
曾文平 《应用数学和力学(英文版)》2000,21(9):1071-1078
IntroductionThispaperdealswiththeinitial_boundaryvalueproblemofthree_dimensionalheatconductionequationintheregionD :0≤x,y ,z≤L ,0 ≤t≤T u t= 2 u x2 2 u y2 2 u z2 ,u|x=0 =f1(y,z,t) , u|x=L =f2 (y ,z,t) ,u|y=0 =g1(z,x,t) , u|y=L =g2 (z,x,t) ,u|z=0 =h1(x ,y ,t) , u|z=L =h2 (x ,y ,t) ,u|t=0 =φ(x ,y,z) .(1 )(2 )… 相似文献
12.
This paper presents the application of Moire interferometry in measuring the displacement and strain field at notch-tip and
crack-tip before and after crack propagation. The experiment is carried out using a three point bending beam with a notch.
TheN
x andN
y fringe patterns representing displacement field, and the ΔN
x/Δx and ΔN
γ/Δγ fringe patterns representing the strain field are obtained. The sensitivity of the measured displacement is 0.417 μm per
fringe order. The displacement and strain distribution along the sectionx=0 have been worked out according toN
x andN
γ fringe patterns.
The project supported by Chinese Academy of Sciences and National Natural Science Foundation of China 相似文献
13.
M. Parvazinia V. Nassehi R. J. Wakeman M. H. R. Ghoreishy 《Transport in Porous Media》2006,63(1):71-90
Despite the widespread use of the Darcy equation to model porous flow, it is well known that this equation is inconsistent
with commonly prescribed no slip conditions at flow domain walls or interfaces between different sections. Therefore, in cases
where the wall effects on the flow regime are expected to be significant, the Darcy equation which is only consistent with
perfect slip at solid boundaries, cannot predict velocity and pressure profiles properly and alternative models such as the
Brinkman equation need to be considered. This paper is devoted to the study of the flow of a Newtonian fluid in a porous medium
between two impermeable parallel walls at different Darcy parameters (Da). The flow regime is considered to be isothermal and steady. Three different flow regimes can be considered using the Brinkman
equation: free flow (Da > 1), porous flow (high permeability, 1 > Da > 10−6) and porous flow (low permeability Da < 10−6). In the present work the described bench mark problem is used to study the effects of solid walls for a range of low to
high Darcy parameters. Both no-slip and slip conditions are considered and the results of these two cases are compared. The
range of the applicability of the Brinkman equation and simulated results for different cases are shown. 相似文献
14.
Large-Eddy simulations (LES) of spatially evolving turbulent buoyant round jets have been carried out with two different density
ratios. The numerical method used is based on a low-Mach-number version of the Navier–Stokes equations for weakly compressible
flow using a second-order centre-difference scheme for spatial discretization in Cartesian coordinates and an Adams–Bashforth
scheme for temporal discretization. The simulations reproduce the typical temporal and spatial development of turbulent buoyant
jets. The near-field dynamic phenomenon of puffing associated with the formation of large vortex structures near the plume
base with a varicose mode of instability and the far-field random motions of small-scale eddies are well captured. The pulsation
frequencies of the buoyant plumes compare reasonably well with the experimental results of Cetegen (1997) under different
density ratios, and the underlying mechanism of the pulsation instability is analysed by examining the vorticity transport
equation where it is found that the baroclinic torque, buoyancy force and volumetric expansion are the dominant terms. The
roll-up of the vortices is broken down by a secondary instability mechanism which leads to strong turbulent mixing and a subsequent
jet spreading. The transition from laminar to turbulence occurs at around four diameters when random disturbances with a 5%
level of forcing are imposed to a top-hat velocity profile at the inflow plane and the transition from jet-like to plume-like
behaviour occurs further downstream. The energy-spectrum for the temperature fluctuations show both −5/3 and −3 power laws,
characteristic of buoyancy-dominated flows. Comparisons are conducted between LES results and experimental measurements, and
good agreement has been achieved for the mean and turbulence quantities. The decay of the centreline mean velocity is proportional
to x
−1/3 in the plume-like region consistent with the experimental observation, but is different from the x
−1 law for a non-buoyant jet, where x is the streamwise location. The distributions of the mean velocity, temperature and their fluctuations in the near-field
strongly depend upon the ratio of the ambient density to plume density ρa/ρ0. The increase of ρa/ρ0 under buoyancy forcing causes an increase in the self-similar turbulent intensities and turbulent fluxes and an increase
in the spatial growth rate. Budgets of the mean momentum, energy, temperature variance and turbulent kinetic energy are analysed
and it is found that the production of turbulence kinetic energy by buoyancy relative to the production by shear is increased
with the increase of ρa/ρ0.
Received 16 June 2000 and accepted 26 June 2001 相似文献
15.
Ma Mingshu 《应用数学和力学(英文版)》1998,19(5):497-501
In this paper, a new three-level explicit difference scheme with high-orderaccuracy is proposed for solving three-dimensional parabolic equations. The stabilitycondition is r=△t/△x2 =△t/△y2=△t/△z2≤1/4, and the trumcation error is O(△t2+△x4). 相似文献
16.
A high order of asymptotic solution of the singular fields near the tip of a mode III interface crack for pure power-law hardening
bimaterials is obtained by using the hodograph transformation. It is found that the zero order of the asymptotic solution
corresponds to the assumption of a rigid substrate at the interface, and the first order of it is deduced in order to satisfy
completely two continuity conditions of the stress and displacement across the interface in the asymptotic sense. The singularities
of stress and strain of the zeroth order asymptotic solutions are −1/(n
1+1) and −n/(n
1+1) respectively. (n=n
1,n
2 is the hardening exponent of the bimaterials.) The applicability conditions of the asymptotic solutions are determined for
both zeroth and first orders. It is proved that the Guo-Keer solution[10] is limited in some conditions. The angular functions of the singular fields for this interface crack problem are first expressed
by closed form.
The project supported by National Natural Science Foundation of China 相似文献
17.
18.
《Wave Motion》1987,9(2):171-190
Four two-dimensional configurations are considered in this paper. The first two concern a homogeneous slab (0⩽y⩽H, −∞<x<∞), with a surface-breaking crack (x=0, 0⩽y⩽a), and without such a crack. The other two configurations concern semi-infinite slabs of different mechanical properties which are in welded contact over x=0, 0⩽y⩽H. One of these has a surface-breaking crack in the interface (x=0, 0⩽y⩽a), and the other has perfect contact over the whole interface. Results are presented for diffraction and corner reflection of an ultrasonic displacement pulse. Time-domain calculations have been carried out bu the use of the finite difference method. The results are presented as full-field snapshots of the displacement fields at specified times, and as time histories of the particle velocity at the midpoint of the transducer-specimen interface at x=−H, y=H. 相似文献
19.
I. H. Stampouloglou E. E. Theotokoglou 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,75(1):1-17
In this study, the generally anisotropic and angularly inhomogeneous wedge under a monomial type of distributed loading of
order n of, the radial coordinate r at its external faces is considered. At first, using variable separable relations in the equilibrium equations, the strain–stress
relations and the strain compatibility equation, a differential system of equations, is constructed. Decoupling this system,
an ordinary differential equation is derived and the stress and displacement fields may be determined. The proposed procedure
is also applied to the elastostatic problem of an isotropic and angularly inhomogeneous wedge. The special cases of loading
of order n=−1 and n=−2, where the self-similarity approach is not valid, are examined and the stress and displacements fields are derived. Applications
are presented for the cases of an angularly inhomogeneous wedge and in the case of a bi-material isotropic wedge. 相似文献
20.
《European Journal of Mechanics - A/Solids》2000,19(3):525-534
This paper examines the axisymmetric problem pertaining to a penny-shaped crack which is located at the bonded plane of two similar elastic halfspace regions which exhibit localized axial variations in the linear elastic shear modulus, which has the form G(z)=G1+G2e±ζz. The equations of elasticity governing this type of non-homogeneity are solved by employing a Hankel transform technique. The resulting mixed boundary value problem associated with the penny-shaped crack is reduced to a Fredholm integral equation of the second kind which is solved in a numerical fashion to generate the crack opening mode stress intensity factor at the tip. 相似文献