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1.
This paper studies a numerical solution of multiple crack problem in a finite plate using coupled integral equations. After using the principle of superposition, the multiple crack problem in a finite plate can be converted into two problems: (a) the multiple crack problem in an infinite plate and (b) a usual boundary value problem for the finite plate. For the former problem, the Fredholm integral equation is used. For the latter problem, a BIE based on complex variable is suggested in which a Cauchy singular kernel exists. For the proposed BIE, after using the inverse matrix technique, the dependence of the traction at a domain point from the boundary tractions is formulated indirectly. This is a particular advantage of the present study. Several numerical examples are provided and the computed results for stress intensity factor and T-stress at crack tips are given. 相似文献
2.
《International Journal of Solids and Structures》2007,44(21):6860-6877
Within the scope of linear elasticity, an in-plane problem related to the repair of an infinite thin elastic plate with a hole by a patch is considered. The patch and the plate are joined together only along their boundaries. The plate is subjected to stresses applied at infinity. The problem is reduced to a system of four singular integral equations. Existence and uniqueness of the solution of the system is proved. The proposed solution allows one to evaluate the efficiency of a patch repair with little computational effort. 相似文献
3.
M. Medved’ 《Nonlinear Oscillations》2008,11(1):70-79
We deal with an integral inequality with a power nonlinearity on its left-hand side, n nonlinearities on its right-hand side, and weakly singular kernels. The obtained result is an extension of the Bihari, Henry,
Pachpatte, and Pinto inequalities and results obtained by the author. Using these results, we prove sufficient conditions
for the existence of global solutions of some nonlinear Volterra integral equations with singular kernels and n nonlinearities.
Published in Neliniini Kolyvannya, Vol. 11, No. 1, pp. 71–80, January–March, 2007. 相似文献
4.
V. N. Buivol 《International Applied Mechanics》2006,42(2):145-151
A mathematical model of the hydrodynamics of free closed surfaces in a fluid is expounded. It is used for studying the dynamics
of ellipsoidal cavities during their development. The model is based on a system of differential equations that accounts for
the influence exerted on the dynamics of cavities by various perturbations such as gravity, surface tension, viscosity, and
geometrical features of the cavity. Solving this system makes it possible to determine the hydrodynamic characteristics of
the flow around the cavity and to plot cavity shapes depending on time and flow regimes. Characteristic features of the development
of such cavities under gravity and surface tension are established
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 24–31, February 2006. 相似文献
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An exact solution of a four part mixed boundary value problem representing a three colinear crack system connected with specified crack opening displacements between the cracks is obtained. The three cracks thus become one with pressure and/or opening displacement prescribed on the crack face. From considerations of dual symmetry and a formulation based on Papkovich-Neuber harmonic functions, the boundary value problem is reduced to solving a quadruple set of integral equations. An exact solution of these equations is derived using a modified finite Hilbert transform technique. The closed form results for the stress distributions and the crack-tip stress intensity factors are presented. Limiting cases of the solution yield results which agree with well known solutions. 相似文献
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The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000. 相似文献
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10.
Erik B. Hansen 《Journal of Elasticity》1976,6(1):39-56
Two integral equation formulations for the determination of the vertical displacement and the bending moment around holes in an elastic plate are presented. Each formulation consists of two equations, the first one an integral equation and an integro-differential equation and the second one two singular integral equations. The equations are solved using B-splines as approximations to the unknowns and the method is applied to the case of one elliptic hole in a twisted plate.
An abbreviated version of this paper was included in a paper Integral equation solutions to mechanical problems. A review and an application to plate theory which will appear in the Proceedings from second national congress of theoretical and applied mechanics, Druzba, Bulgaria, 1973. 相似文献
Zusammenfassung Zwei verschiedene Integralgleichungssysteme für die Bestimmung von die Durchbiegung und die Biegemoment in einer gelochten elastischen Platte werden entwickelt. Die eine Systeme besteht von einer Integralgleichung und einer Integro-Differentialgleichung und die andere von zwei singulären Integralgleichungen von Cauchy'schen Typus. Bei der Auflösung der Systeme werden die unbekannten mit Hilfe B-splines ausgedrückt. Beide Systeme werden benutzt in dem Fall von einer elliptischen Loch in einer uendlichen, tordierten Platte.
An abbreviated version of this paper was included in a paper Integral equation solutions to mechanical problems. A review and an application to plate theory which will appear in the Proceedings from second national congress of theoretical and applied mechanics, Druzba, Bulgaria, 1973. 相似文献
11.
This paper is taken up for the following difference equation problem(P,)(L,y)_k≡εy(k 1) a(k,ε)y(k) b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1),B_1y≡-y(0) c_1y(1)=a,B_2y≡-c_2y(N-1) y(N)=βwhereεis a small parameter,c_1,c_2,a,βconstants and a(k,ε),b(k,ε),f(k,ε)(1≤k≤N)functions of k andε.Firstly,the case with constant coefficients isconsidered.Secondly,a general method based on extended transformation is given tohandle(P.)where the coefficients may be variable and uniform asymptotic expansionsare obtained Finally,a numerical example is provided to illustrate the proposed method. 相似文献
12.
N. I. Ioakimidis 《Journal of Elasticity》1985,15(3):325-333
The method of singular integral equations is an efficient method for the formulation and numerical solution of plane and antiplane, static and dynamic, isotropic and anisotropic elasticity problems. Here we consider three cases of singular loadings of the elastic medium: by a force, by a moment and by a loading distribution with a simple pole. These loadings cause corresponding singularities in the right-hand side function and in the unknown function of the integral equation. A method for the numerical solution of the singular integral equation under the above singular loadings is proposed and the validity of this equation at the singular points is investigated. 相似文献
13.
G. M. L. Gladwell 《Journal of Elasticity》1992,28(2):97-109
It is shown that the coupled singular integral equations with trigonometric kernels appearing in the problem of adhesive contact between an elastic circular cylinder and two identical rigid compressive rollers may be reduced to a problem of Muskhelishvili type and may be explicitly solved. The solution is applied to the cases when the rollers are either flat or circular, and the results are compared with those found by Hill and Tordesillas [2]. 相似文献
14.
Nonlinear Dynamics - In this paper, the $$(G'/G)$$ -expansion method is employed to construct more general solitary wave solutions of three special types of Boussinesq equation, namely... 相似文献
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Summary The paper deals with numerical solutions of singular integral equations in stress concentration problems for longitudinal
shear loading. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy-type
singularities, where unknown functions are densities of body forces distributed in the longitudinal direction of an infinite
body. First, four kinds of fundamental density functions are introduced to satisfy completely the boundary conditions for
an elliptical boundary in the range 0≤φ
k
≤2π. To explain the idea of the fundamental densities, four kinds of equivalent auxiliary body force densities are defined
in the range 0≤φ
k
≤π/2, and necessary conditions that the densities must satisfy are described. Then, four kinds of fundamental density functions
are explained as sample functions to satisfy the necessary conditions. Next, the unknown functions of the body force densities
are approximated by a linear combination of the fundamental density functions and weight functions, which are unknown. Calculations
are carried out for several arrangements of elliptical holes. It is found that the present method yields rapidly converging
numerical results. The body force densities and stress distributions along the boundaries are shown in figures to demonstrate
the accuracy of the present solutions.
Received 26 May 1998; accepted for publication 27 November 1998 相似文献
17.
羊丹平 《应用数学和力学(英文版)》1986,7(12):1189-1201
In this paper we consider the singular perturbation boundary-value problem of thefollowing coupling type system of convection-diffusion equationsWe advance two methods:the first one is the initial value solving method,by which theoriginal boundary-value problem is changed into a series of unperturbed initial-valueproblems of the first order ordinary differential equation or system so that an asymptoticexpansion is obtained;the second one is the boundary-value solving method,by which theoriginal problem is changed into a few boundary-value problems having no phenomenon ofboundary-layer so that the exact solution can be obtained and any classical numericalmethods can be used to obtain the numerical solution of consismethods can be used to obtainthe numerical solution of consistant high accuracy with respect to the perturbationparameterε 相似文献
18.
Jean-Claude Nedelec 《国际流体数值方法杂志》1987,7(11):1229-1234
We present some integral methods for exterior problems for the Laplace equation. Then we give finite element approximations for these equations and some errors estimates. Finally, we indicate how these integral equations can be coupled with a usual finite element method on a bounded domain to solve an exterior non-linear problem which is linear far away. 相似文献
19.
H.D. Bui 《Journal of the mechanics and physics of solids》1977,25(1):29-39
The problem of a plane crack of arbibrary shape, subjected to arbitrary loading, is studied. The displacement field is represented by two elastic potentials, the single-layer and the double-layer potential of the second kind. The equations for the crack displacement discontinuities are derived. An approximate analysis of the crack opening displacement under pressure is discussed. 相似文献
20.
Stress intensity factors for a three dimensional rectangular interfacial crack were considered using the body force method. In the numerical calculations, unknown body force densities were approximated by the products of the fundamental densities and power series; here the fundamental densities are chosen to express singular stress fields due to an interface crack exactly. The calculation shows that the numerical results are satisfied. The stress intensity factors for a rectangular interface crack were indicated accurately with the varying aspect ratio, and bimaterial parameter. 相似文献