共查询到19条相似文献,搜索用时 46 毫秒
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直接边界元法中边界积分的解析处理 总被引:6,自引:1,他引:5
确立了平面位势和弹性力学问题的边界元直接法中边界积分的解析计算框架系统,从而避免了传统的主似求积分,数值算例表胆它具有较高的精度和效率,特别是在边界量和边界附近区域内点物理量的计算可获得较高的精度。 相似文献
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利用变分法证明平面调和函数的外问题的确切形式;在此基础上,建立外问题的具有间接变量的等价边界积分方程;传统的外问题及边界积分方程不具有普遍适用性,本文对此进行了详细的讨论. 相似文献
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1.引 言 考虑平面弹性力学内或外位移边值问题和内或外应力边值问题这里Ω是平面有界开集,Ωc是闭包Ω的补集,Γ是Ω或Ωc的边界,u=(u1,u2)是位移,n=(n1,n2)是Γ的外法向单位向量,δij=(ui,j+uj,i)/2是应变张量,λ和μ是Lame常数,并且按张量计算规则:重复下标蕴含对该下标从1到2的求和. 使用直接边界元方法(1.1)与(1.2)皆可被转换为边界积分方程组这里αij(y)是取决于y∈Γ的常数,当y是Γ的光滑点时,;式中是kelvin基本解,有以下表达式[5,7]这里r=… 相似文献
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张耀明 《纯粹数学与应用数学》2001,17(1):28-34
确立平面位势和弹性力学问题的边界元直接法中边界积分的解析计算框架系统,从而避免了传统的高斯近似求积分,数值算例表明它具有较高的精度和效率,特别是在边界量和边界附近区域内点物理量的计算可获得较高的精度。 相似文献
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本文对两个非均匀半平面粘结的非均匀平面的裂纹问题作了分析,文中假定两种材料的泊松比v相同,但杨氏模量随坐标x按不同形式的指数函数变化.本文使用非均匀平面问题的单裂纹解及富氏变换方法, 使问题归为一个柯西型奇异积分方程,最后对应力强度因子的计算给出了若干数值例子. 相似文献
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The accuracy of standard boundary element methods for elliptic boundary value problems deteriorates if the boundary of the domain contains corners or if the boundary conditions change along the boundary. Here we first investigate the convergence behaviour of standard spline Galerkin approximation on quasi-uniform meshes for boundary integral equations on polygonal domains. It turns out, that the order of convergence depends on some constant describing the singular behaviour of solutions near corner points of the boundary. In order to recover the full order of convergence for the Galerkin approximation we propose the dual singular function method which is often used for improving the accuracy of finite element methods. The theoretical convergence results are confirmed and illustrated by a numerical example. 相似文献
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D. S. Anikonov 《Siberian Mathematical Journal》2010,51(5):765-775
We examine a singular integral equation of the first kind on a bounded open set of an n-dimensional space. Open subsets with
a common (contact) (n — 1)-dimensional piecewise smooth part of boundaries are selected. The underdetermined case is treated
in which the unknown part of the integrand depends on 2n independent variables whereas a given integral depends only on n
variables. In this situation we pose the problem of finding the contact part of the boundaries and prove unique solvability
of the problem. 相似文献
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This paper deals with the solvability of boundary value problems for singular integral equations of the form (i)-(ii).By an algebraic method we reduce the problem (i)-(ii) to a system of linear algebraic equations which gives all solutions in a closed form.AMS Subject Classification: 47G05, 45GO5, 45E05 相似文献
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某些带变换的边值问题和奇异积分方程 总被引:3,自引:0,他引:3
本文主要考虑某些带变换的奇异积分方程。尽管用经典的正则化方法可以求解,我们还是给出一种新的分区跳跃方法,使它们化为较简单的可以系统地求解并可迅即讨论的Fredholm积分方程。 相似文献
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Ulrich Schmid 《Mathematische Nachrichten》1995,174(1):273-282
The classical polynomial collocation method is considered for a class of Cauchy singular integral equations with variable coefficients on a bounded interval. This method is naturally extended to the case of a non-zero index of the underlying Fredholm operator. This is done by using the structure of the kernel and a complement of the image of this operator. For the extended method we directly obtain error bounds in the norm of the weighted Holder spaces. As an illustration, some numerical results are given. 相似文献
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In the study interface cracks between two dissimilar homogeneous isotropic half-spaces undergoing impact loading are considered. The problem is solved using the boundary integral equations in the frequency domain. The distributions of the displacements and tractions at the bonding interface and surfaces of the cracks are obtained and analyzed. The stress intensity factors (opening and shear modes) are computed for different load conditions and various properties of the bimaterial. The results are compared with the ones obtained in the time domain. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The boundary element method (BEM) is developed and applied in new fields of dynamic fracture mechanics, dynamics of composite, elasto–plastic and piezoelectric materials. The BEM results are compared with solutions computed by the finite element method (FEM) showing high accuracy of the BEM. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献