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1.
证明面力边界积分方程被积函数的散度等于零,应用Stokes公式,对平面线弹性问题,将面力边界积分的求解转化为边界点的位移势函数的点值计算。应用边界积分方程的求解结果,推导出J积分亦可表示为边界点的积分势函数的点值计算,无需进行数值积分,实例计算说明该方法的有效性。 相似文献
2.
From the point of view of energy analysis,the cause that the uniqueness of theboundary integral equation induced from the exterior Helmholtz problem does not hold isinvestigated in this paper.It is proved that the Sommerfeld’s condition at the infinity ischanged so that it is suitable not only for the radiative wave but also for the absorptive wavewhen we use the boundary integral equation to describe the exterior Helmholtz problem.Therefore,the total energy of the system is conservative.The mathematical dealings toguarantee the uniqueness are discussed based upon this explanation 相似文献
3.
In this paper, we propose a new boundary integral equation for plane harmonic functions. As a new approach, the equation is
derived from the conservation integrals. Every variable in the integral equation has direct engineering interest. When this
integral equation is applied to the Dirichlet problem, one will get an integral equation of the second kind, so that the algebraic
equation system in the boundary element method has diagonal dominance. Finally, this equation is applied to elastic torsion
problems of cylinders of different sections, and satisfactary numerical results are obtained. 相似文献
4.
Y. Z. Chen X. Y. Lin Z. Q. Peng 《Archive of Applied Mechanics (Ingenieur Archiv)》1998,68(3-4):271-280
Summary A hypersingular integral equation or a differential-integral equation is used to solve the penny-shaped crack problem. It
is found that, if a displacement jump (crack opening displacement COD) takes the form of (a
2−x
2−y
2)1/2
x
m
y
n
, where a denotes the radius of the circular region, the relevant traction applied on the crack face can be evaluated in a closed form,
and the stress intensity factor can be derived immediately. Finally, some particular solutions of the penny-shaped crack problem
are presented in this paper.
Received 1 July 1997; accepted for publication 13 October 1997 相似文献
5.
G. Tsamasphyros D. A. Eftaxiopoulos 《Archive of Applied Mechanics (Ingenieur Archiv)》1996,66(7):434-446
Summary The exact solution of the problem of a dislocation interacting with a crack has been used for the generation of integral equations on the microcracks only. A few discresation points are needed along the microcracks, due to their small length. The solution of the resulting system of linear algebraic equations is effected via interations for the time of computations to be further reduced. In several cases our results seem to be more accurate than the ones obtained in [3]. 相似文献
6.
Dr. T. Zlatanovski 《Archive of Applied Mechanics (Ingenieur Archiv)》1995,65(5):346-364
Summary A boundary integral equation method is proposed for approximate numerical and exact analytical solutions to fully developed incompressible laminar flow in straight ducts of multiply or simply connected cross-section. It is based on a direct reduction of the problem to the solution of a singular integral equation for the vorticity field in the cross section of the duct. For the numerical solution of the singular integral equation, a simple discretization of it along the cross-section boundary is used. It leads to satisfactory rapid convergency and to accurate results. The concept of hydrodynamic moment of inertia is introduced in order to easily calculate the flow rate, the main velocity, and the fRe-factor. As an example, the exact analytical and, comparatively, the approximate numerical solution of the problem of a circular pipe with two circular rods are presented. In the literature, this is the first non-trivial exact analytical solution of the problem for triply connected cross section domains. The solution to the Saint-Venant torsion problem, as a special case of the laminar duct-flow problem, is herein entirely incorporated. 相似文献
7.
When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM),singularities in the local boundary integrals need to be treated specially. In the current paper,local integral equations are adopted for the nodes inside the domain trod moving least square approximation (MLSA) for the nodes on the global boundary,thus singularities will not occur in the new al- gorithm.At the same time,approximation errors of boundary integrals are reduced significantly.As applications and numerical tests,Laplace equation and Helmholtz equa- tion problems are considered and excellent numerical results are obtained.Furthermore, when solving the Hehnholtz problems,the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions.Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number. 相似文献
8.
Research on the companion solution for a thin plate in the meshless local boundary integral equation method 总被引:1,自引:1,他引:0
The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method ( GFEM ), boundary element method (BEM) and element free Galerkin method (EFGM), and is a truly meshless method possessing wide prospects in engineeringapplications. The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem. 相似文献
9.
10.
SOLVINGVIBRATIONPROBLEMOFTHINPLATESUSINGINTEGRALEQUATIONMETHOD¥(许明田,程德林)XuMingtian;ChengDelin(Department.ofMathematicsandPhysi... 相似文献
11.
12.
Summary An elementary solution for the multiple circular arc problem is obtained in this paper. The elementary solution is defined
as a particular case of the single circular arc crack problem, in which remote stresses are equal to zero, and two pairs of
concentrated forces are applied at a prescribed point of crack face. By using the principle of superposition, Fredholm integral
equation for the multiple circular arc problem in plane elasticity is obtained. The suggested approach is illustrated by several
numerical examples. If a smaller arc crack is surrounded by a larger arc crack, the stress intensity factors for the former
become rather small. The phenomenon of shielding is illustrated by examples.
Accepted for publication 17 September 1996 相似文献
13.
Hu Haichang 《Acta Mechanica Sinica》1992,8(2):127-135
A boundary integral representation of plane biharmonic function is established rigorously by the method of unanalytical continuation
in the present paper. In this representation there are two boundary functions and four constants which bear a one to one correspondence
to biharmonic functions. Therefore the set of boundary integral equations with indirect unknowns based on this representation
is equivalent to the original differential equation formulation. 相似文献
14.
The low-order polynomial-distributed eigenstrain formulation of the boundary integral equation (BIE) and the corresponding
definition of the Eshelby tensors are proposed for the elliptical inhomogeneities in two-dimensional elastic media. Taking
the results of the traditional subdomain boundary element method (BEM) as the control, the effectiveness of the present algorithm
is verified for the elastic media with a single elliptical inhomogeneity. With the present computational model and algorithm,
significant improvements are achieved in terms of the efficiency as compared with the traditional BEM and the accuracy as
compared with the constant eigenstrain formulation of the BIE. 相似文献
15.
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
16.
17.
将弹性力学平面问题归化成无奇异边界积分方程,避免了传统的边界元法中的柯西主值(CPV)积分和Hadamard-Finite-Parts(HFP)积分的计算,建立完整的数值求解体系。 相似文献
18.
By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing. 相似文献
19.
20.
In this paper, the basic presentation in antiplane shear and inplane electric field of piezoelectric materials is refreshed.
In order that the functions used in the formulation can be distinguished by their usage, four analytic functions, or four
complex potentials, are introduced. A multiple crack problem for piezoelectric materials is studied. After taking the traction
or the electric displacement on the crack face as unknown functions, one can naturally obtain a Fredholm integral equation
for the multiple crack problem. It is found that the Fredholm integral equation approach is effective for solving the multiple
crack problem. Finally, numerical examples are given. 相似文献