共查询到19条相似文献,搜索用时 109 毫秒
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用变分法证明平面弹性力学外边值问题的正确提法。在此基础之上,确立外问题的等价的直接变量边界积分方程。对传统的惯用的直接变量边界积分方程进行了深入的讨论,表明它与原边值问题不等价。 相似文献
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平面Laplace外边值问题 总被引:5,自引:3,他引:2
证明平面调和函数的Dirichlet外问题解存在唯一的充要条件,在此基础上,确立外问题的等价边界积分方程,首次给出外域上的极值原理,对第一类Fredholm边界的积分方程的可解性进行了讨论。 相似文献
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本文针对各向异性势问题提出了一类充分必要的随机边界积分方程,数值计算结果表明在退化尺度附近,充要的随机边界积分程较习用的随机边界积分方程有较大的优越性。 相似文献
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文[4]导出了二维弹性力学平面问题的一类新型边界积分方程,本文将该理论和方法推广到三变量的Reissner板弯曲中,给出边界场变量含广义位移和新型广义力的边界积分方程。从而边界弯矩应力张量可直接由离散边界积分方程求出。 相似文献
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本文讨论二维弹性力学平面问题,独立于Rizzo型边界分方程,一类新型的边界积分方程,其边界场变量包含应力分量σijtitj(其中ti是边界切向余弦)。该应力分量可直接用数值方法解边界积分方程求出,它比常规的边界元解提高一阶精度。文末的算例表明确定论的实用性和有效性。 相似文献
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弹性薄板弯曲问题的等价的直接变量边界积分方程 总被引:1,自引:0,他引:1
建立平面弹性薄板弯曲问题理论中具有直接变量的等价边界积分方程,传统的直接变量边界积分方程,它们都不是等价的,对此进行了深入的讨论。 相似文献
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In this paper, the artificial boundary method is considered for the numerical simulation of the exterior Stokes flow in three dimensions. First, an exact relation between the normal stress and the velocity field is obtained on a spherical artificial boundary. With the relation specified on the artificial boundary, the original problem is reduced to a new one only defined on a finite domain. After that, an variational problem equivalent to the reduced problem is derived. By truncating the series term in the formulation, a sequence of approximate variational problems are obtained, which can then be solved with a suitable finite‐element scheme. Finally, a numerical example is presented to show the performance of the method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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IntroductionIthasbeenratheralonghistorythattheBoundaryElementMethod (BEM )isappliedtosolvetheplaneelasticityproblems[1~2 ].However,theEBIE ,whichisequivalenttotheoriginalboundaryvalueproblem ,hasnotbeenfullyappreciatedandsolvedinBEMcommunity .TheconventionalboundaryintegralequationswithindirectvariablesarediscussedthoroughlyanditisshownthatthepreviousresultsarenotEBIE ,i.e .,sometimes,thereexistsnosolutionormorethanonesolutiontothem .Themainkeyliesintheexactformoftheexteriorproblems.I… 相似文献
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V. N. Belykh 《Journal of Applied Mechanics and Technical Physics》2006,47(5):661-670
Based on Babenko’s fundamental mathematical ideas, principally new (unsaturated) algorithms are developed for the numerical
solution of problems of a potential axisymmetric ideal fluid flow around bodies of revolution, in particular, an ellipsoid
of revolution with an aspect ratio equal to 1000.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 56–67, September–October, 2006. 相似文献
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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
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复数矢径虚拟边界谱方法在二维空穴声辐射和散射问题中的应用 总被引:1,自引:1,他引:0
基于复数矢径虚拟边界积分法,通过将虚拟积分曲线上的未知源强密度函数用Fourier级数展开,同时借助快速数值Fourier变换计算程序,提出了一种求解二维任意形状空穴声辐射和散射问题的复数矢径虚拟边界谱方法.该方法具有以下特点:(1)不存在奇异积分处理;(2)采用复数矢径虚拟边界积分方法,不仅保证了解的唯一性,而且由于虚拟源强密度函数采用Fourier级数展开,克服了用单元离散方法不能用于较高频率范围的缺点;(3)采用快速数值Fourier变换技术使计算效率大幅度提高.文中给出的计算结果表明:在求解任意形状二维空穴声辐射和散射问题上较通常采用的FEM、BEM和VBEM更为有效. 相似文献
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伸缩虚拟边界元法解二维Helmholtz外问题 总被引:1,自引:0,他引:1
以位势理论为基础,提出了求解Helmholtz外问题的伸缩虚拟边界元法.给出了该方法在全波数域内获得唯一解的严格数学证明,其核心是通过伸缩虚拟边界使对偶内问题的特征频率(本征值)避开与波数重合,从而保证了解的唯一性,同以往前人提出的几种解法途径相比,该法简单得多;通过诸多边界曲线形状和不同边界量的声辐射算例,从计算精度、稳定性以及克服解的非唯一性等方面,对该方法进行了检验.计算结果表明:对远场或近场辐射声压,该方法都具有非常高的效率和精度. 相似文献
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本文首先简要介绍Bcklund变换理论的发展过程,然后介绍一种寻找微分方程Bcklund变换的新方法——wahlquist-Estabrook过程。该方法是目前处理微分方程Bcklund问题的最有效方法.尽管该方法在理论上可应用于任意维数的偏微分方程组,但是实际上它所能处理的主要是二维问题。例如,在应用该方法处理完整Navicr-Stokcs方程(四维问题)时,所得到的是无意义结果.但是,在应用该方法处理定常二维Navicr-Stokcs方程时,确实可以得到正常的Bcklund映射,以及Bcklund变换. 相似文献
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Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational
principle. Two aggregate-function-based algorithms for solving complementarity problems are proposed. One is called the self-adjusting
interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency
of the proposed two algorithms.
The project supported by the National Natural Science Foundation of China(10225212, 50178016, 10302007), the National Key
Basic Research Special Foundation and the Ministry of Education of China The English text was polished by Ron Marshall. 相似文献
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It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all. 相似文献