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SINGULAR INTEGRAL EQUATIONS AND BOUNDARY ELEMENT METHOD OF CRACKS IN THERMALLY STRESSED PLANAR SOLIDS
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作者 徐春晖 秦太验 华云龙 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第4期399-406,共8页
Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, a... Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, and then,its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation, and the singular temperature gradients are exactly obtained. Finally, several typical examples calculated. 展开更多
关键词 heat transfer CRACK singular integral equation boundary element method stress intensity factor
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Improved non-singular local boundary integral equation method
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作者 付东杰 陈海波 张培强 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第8期1093-1099,共7页
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 p... 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 and 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 equation problems are considered and excellent numerical results are obtained. Furthermore, when solving the Helmholtz 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. 展开更多
关键词 meshless method local boundary integral equation method moving least square approximation singular integrals
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To Theory One Class Linear Model Noclassical Volterra Type Integral Equation with Left Boundary Singular Point
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作者 Nusrat Rajabov 《Applied Mathematics》 2013年第9期1301-1312,共12页
In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of... In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of the signs parameters solution to this integral equation can contain three arbitrary constants, two arbitrary constants, one constant and may have unique solution. In the case when general solution of integral equation contains arbitrary constants, we stand and investigate different boundary value problems, when conditions are given in singular point. Besides for considered integral equation, the solution found cane represented in generalized power series. Some results obtained in the general model case. 展开更多
关键词 NEOCLASSICAL VOLTERRA Type integral equation LEFT boundary singular Point boundary Value Problems
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RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
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作者 Reinhard Hochmuth (Freie Universitat Berlin, Germany) 《Approximation Theory and Its Applications》 2002年第1期1-25,共25页
This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterization... This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results. 展开更多
关键词 In RESTRICTED NONLINEAR APPROXIMATION AND singular SOLUTIONS OF boundary integral equationS
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Integral Representation of the Manifold Solution for New Class of the Volterra Type Integral Equation with a Boundary Singularity in the Case, When Kernel Contain Logarithmic Singularity and its Power
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作者 Nusrat Rajabov 《Journal of Mathematics and System Science》 2016年第1期23-37,共15页
In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity an... In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at n = 2m reduce to problem investigate the Volterra type integral equation (1) for n = 2 the theory for which was constructed in [2]. In this work, we investigation integral equation (1) at = 2m + 1 In this case, we investigate integral equation (1) reduction it's to m integral equation type [2] φ(x)+∫xa[p1+p2 ln(x-a/t-a)]φ(t)/t-a dt=f(x)and one the following integral equation [1] ω(x)+p3∫xω(t)/ a t-adt=g(x). 展开更多
关键词 singular kernel volterra type integral equation boundary singularity logarithmic singularity.
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BOUNDARY INTEGRAL EQUATIONS FOR THE BENDING PROBLEM OF PLATES ON TWO-PARAMETER FOUNDATION 被引量:2
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作者 李正良 邓安福 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第7期657-667,共11页
By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is exp... By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series. On the basis of the above work, two boundary integral equations which are suitable to arbitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem. 展开更多
关键词 Bending (deformation) boundary element method Convergence of numerical methods Fourier transforms integral equations
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A Direct Implementation of a Modified Boundary Integral Formulation for the Extended Fisher-Kolmogorov Equation 被引量:3
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作者 Okey Oseloka Onyejekwe 《Journal of Applied Mathematics and Physics》 2015年第10期1262-1269,共8页
This study is concerned with the numerical approximation of the extended Fisher-Kolmogorov equation with a modified boundary integral method. A key aspect of this formulation is that it relaxes the domain-driven appro... This study is concerned with the numerical approximation of the extended Fisher-Kolmogorov equation with a modified boundary integral method. A key aspect of this formulation is that it relaxes the domain-driven approach of a typical boundary element (BEM) technique. While its discretization keeps faith with the second order accurate BEM formulation, its implementation is element-based. This leads to a local solution of all integral equation and their final assembly into a slender and banded coefficient matrix which is far easier to manipulate numerically. This outcome is much better than working with BEM’s fully populated coefficient matrices resulting from a numerical encounter with the problem domain especially for nonlinear, transient, and heterogeneous problems. Faithful results of high accuracy are achieved when the results obtained herein are compared with those available in literature. 展开更多
关键词 boundary element Method EXTENDED Fisher-Kolmogorov equation boundary integral Formulation Slender Coefficient Matrix HYBRIDIZATION Domain-Driven
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Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces 被引量:1
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作者 Shuangxin He Chaoyang Wang +2 位作者 Xuan Zhou Leiting Dong Satya N.Atluri 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第6期1857-1882,共26页
The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engin... The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions. 展开更多
关键词 Symmetric Galerkin boundary element method rotational inertia gravitational force weak singularity stress intensity factor
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EQUIVALENT BOUNDARY INTEGRAL EQUATIONS WITH INDIRECT UNKNOWNS FOR THIN ELASTIC PLATE BENDING THEORY 被引量:1
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作者 张耀明 孙焕纯 杨家新 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第11期1246-1255,共10页
Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical techniq... Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE. 展开更多
关键词 thin plate bending theory boundary element method equivalent boundary integral equations?
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Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations
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作者 马杭 夏利伟 秦庆华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第6期757-767,共11页
A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations (BIE) and solved with the newly developed boundary point method (BPM). The... A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations (BIE) and solved with the newly developed boundary point method (BPM). The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element (RVE), showing the validity and the effectiveness of the proposed computational modal and the solution procedure. 展开更多
关键词 short-fiber equivalent inclusion EIGENSTRAIN Eshelby tensor representative volume element boundary integral equation boundary point method
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REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS
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作者 周焕林 牛忠荣 王秀喜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第10期1208-1214,共7页
A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of ... A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results. 展开更多
关键词 boundary element method (BEM) nearly singular integral REGULARIZATION potential problem
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BOUNDARY INTEGRAL EQUATIONS OF UNIQUE SOLUTIONS IN ELASTICITY
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作者 周慎杰 曹志远 孙树勋 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第10期1128-1133,共6页
The properties of the fundamental solution are derived in linear elastostatics. These properties are used to show that the conventional displacement and traction boundary integral equations yield non-unique displaceme... The properties of the fundamental solution are derived in linear elastostatics. These properties are used to show that the conventional displacement and traction boundary integral equations yield non-unique displacement solutions in a traction boundary value problem. The condition for the existence of unique displacement solutions is proposed for the traction boundary value problem. The degrees of freedom of the displacement solution are removed by the condition to obtain the boundary integral equations of unique solutions for the traction boundary value problems. Numerical example is presented to demonstrate the accuracy and efficiency of the present equations. 展开更多
关键词 boundary integral equation boundary element method ELASTICITY
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A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations
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作者 I.G.Ameen N.A.Elkot +2 位作者 M.A.Zaky A.S.Hendy E.H.Doha 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第7期21-41,共21页
We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional derivatives.The main ingredient of the proposed method is to recast the p... We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional derivatives.The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations.Then,a Legendre-based spectral collocation method is developed for solving the transformed system.Therefore,we can make good use of the advantages of the Gauss quadrature rule.We present the construction and analysis of the collocation method.These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange equations.Two numerical examples are given to confirm the convergence analysis and robustness of the scheme. 展开更多
关键词 Spectral collocation method weakly singular integral equations two-point boundary value problems convergence analysis
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ON THE METHOD OF SOLUTION FOR A KIND OFNONLINEAR SINGULAR INTEGRAL EQUATION 被引量:4
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作者 LuJianke 《Acta Mathematica Scientia》 SCIE CSCD 2004年第3期507-512,共6页
The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obt... The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obtained in [1] when f(t) is a constant. Certain special cases are illustrated. 展开更多
关键词 singular integral equation with Cauchy kernel Riemann boundary value problem with square roots modified principal part Plemelj formula
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The Method of Solutions for some Kinds of Singular Integral Equations of Convolution Type with Both Reflection and Translation Shift 被引量:1
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作者 LI Ping-run 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第1期107-115,共9页
In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coeffici... In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}. 展开更多
关键词 singular integral equation convolution type Riemann boundary value problem REFLECTION translation shift
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Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order
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作者 HAN Hui-li 1,2 ,DU Jin-yuan 1,3 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China 2. School of Mathematics and Computer, Ningxia University, Yinchuan 750021, Ningxia, China 3. Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, China 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第2期339-343,共5页
We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integration is in the strip 0<Rez<aπ. 展开更多
关键词 boundary value problem singular integral equation the singularities of high order
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On a Class of Two Dimensional Singular Integral Equations
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作者 Zhang Zhong-xiang Du Jin-yuan 《Wuhan University Journal of Natural Sciences》 CAS 1999年第2期4-9,共6页
We mainly consider a class of two dimensional normal type singular integral equations, the solutions as well as the conditions of solvability of which are obtained .The methods used consist of transferring them to sev... We mainly consider a class of two dimensional normal type singular integral equations, the solutions as well as the conditions of solvability of which are obtained .The methods used consist of transferring them to several one dimensional Riemann boundary value problems, and then solving the latter. 展开更多
关键词 two dimensional singular integral equations Riemann boundary value problem
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Numeric Simulation of Boundary Element-Volume Element Wave Equation in Complex Geologic Structure
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作者 Yu Geng-xin Li Dong-ping +1 位作者 Fu Li-yun Jiang Tao 《石油地球物理勘探》 EI CSCD 北大核心 2009年第A02期99-105,共7页
关键词 边界元法 数值模拟 复杂地质构造 波动方程 体积元 字符分割 非均质性 建模算法
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A Remark on the Solution for a Certain Nonlinear——Two-Dimenslonal Singular Integral Equation
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作者 Lu De(Central South University of Technology) 《怀化学院学报》 1993年第5期29-32,共4页
The main purpose of this remark is to study the nonlinaer singular integral equation for the unknown function ω(z) of complex variable z in the unit circle G. We obtain the representation of solution for above equation.
关键词 singular integral equation boundary value problen FREDHOLM type equation.
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Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method 被引量:1
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作者 徐春晖 秦太验 +2 位作者 袁丽 野田尚昭 Xing-ming GUO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第3期293-301,共9页
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. I... 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. 展开更多
关键词 stress intensity factor singular integral equation interface crack finite-part integral boundary element method
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