共查询到19条相似文献,搜索用时 68 毫秒
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弹性力学平面问题中一类无奇异边界积分方程 总被引:6,自引:2,他引:6
从理论上提出一种新的方法,归化出间接变量无奇异边界积分方
程. 采用Lagrange二次单元,建立一个数值求解框架系统. 此外,基于问题的计算区域的
特殊性,给出一种边界近似方法. 数值算例表明该方法所取得的数值结果与精确解相当接
近,特别是边界量的数值结果. 此外,该方法容易被推广到三维问题.
和已有的直接变量的情形相比较,具有优点:1)无需处理HFP积分. 大大降低处理问
题的复杂性,并提高了计算效率和解的精度;2)摆脱了问题的具体形式,进入纯代数操作.
这样做的好处是从理论上建立一种普遍适用的方法,不仅适用于弹性力学问题,同样可应用
于其它问题,如位势问题, Stokes问题等. 3)提供了一种计算CPV积分的方法. 相似文献
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论文致力于平面正交各向异性弹性问题的规则化边界元法研究,提出了新的规则化边界元法的理论和方法.对问题的基本解的特性进行了研究,确立基本解的积分恒等式,提出一种基本解的分解技术,在此基础上,结合转化域积分方程为边界积分方程的极限定理,建立了新颖的规则化边界积分方程.和现有方法比,论文不必将问题变换为各向同性的去处理,从而不含反演运算,也有别于Galerkin方法,无需计算重积分,因此所提方法不仅效率高,而且程序设计简单.特别是,所建方程可计算任何边界位移梯度,进而可计算任意边界应力,而不仅限于面力.数值实施时,采用二次单元和椭圆弧精确单元来描述边界几何,使用不连续插值逼近边界函数.数值算例表明,论文算法稳定、效率高,所取得的边界量数值结果与精确解相当接近. 相似文献
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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
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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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给出了正交各向异性平面热弹性问题的边界积分方程、内点应力公式和常单元离散化时计算奇异积分的解析式,计算了正交各向异性板的热应力强度因子,结果表明了文中所导公式的正确性 相似文献
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弹性力学平面问题的等价边界积分方程的边界轮廓法 总被引:5,自引:0,他引:5
基于边界积分方程中被积函数散度为零的特性,提出了弹性力学平面问题的等价边界积分方程的边界轮廓法,该方法无需进行数值积分,只需要计算单元两结点势函数值之差。实例计算说明,基于传统的边界积分方程的边界轮廓法所得到的面力结果是错误,而本文建立的边界轮廓法则可给出精确的结果。 相似文献
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平面问题等价边界积分方程的三次边界轮廓法 总被引:1,自引:0,他引:1
基于弹性力学平面问题等的边界积分方程,给出了三次单元的边界轮廓法。根据平面问题解的复变函数表示,构造了三次形函数。给出了对于混合边值问题求解系统方程确定的边界轮廓方程配置和三次单元界轮廓法的实施。 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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IntroductionIthasbeenratheralonghistorythattheBoundaryElementMethod (BEM )isappliedtosolvetheplaneelasticityproblems[1~2 ].However,theEBIE ,whichisequivalenttotheoriginalboundaryvalueproblem ,hasnotbeenfullyappreciatedandsolvedinBEMcommunity .TheconventionalboundaryintegralequationswithindirectvariablesarediscussedthoroughlyanditisshownthatthepreviousresultsarenotEBIE ,i.e .,sometimes,thereexistsnosolutionormorethanonesolutiontothem .Themainkeyliesintheexactformoftheexteriorproblems.I… 相似文献
12.
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
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The universal practices have been centralizing on the research of regulariza-tion to the direct boundary integal equations (DBIEs). The character is elimination of singularities by using the simple solutions. However, up to now the research of regular ization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value (CPV) and Hadamard-finite-part (HFP) integrals are established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system. 相似文献
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Leonid K. Antanovskii 《Meccanica》1991,26(2-3):59-65
In this paper planar viscous flows with a free boundary are further studied using the quasisteady approximation [1]. The introduction of the bianalytical stress-stream function provides an opportunity to adopt the theory of analytical functions. The mode of construction of the Fredholm boundary integral equations is here proposed through the explicit solutions of two Hilbert problems for holomorphic functions with the application of the conformal mappings. The stabiligy of the equilibrium of the annulus liquid layer is investigated by way of example.
Sommario Si prosegue lo studio di flussi piani viscosi con frontiera libera applicando l'approssimazione quasistazionaria [1]. L'introduzione della funzione stress-stream bianalitica consente l'uso della teoria delle funzioni olomorfe. La costruzione delle equazioni integrali di Fredholm al contorno proposta qui si basa sulla risoluzione esplicita di due problemi di Hilbert per funzioni analitiche mediante applicazione della tecnica delle trasformazioni conformi. Come esempio si studia la stabilità dell'equilibrio di uno strato liquido anulare.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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Hai-Chang Hu 《Acta Mechanica Solida Sinica》1989,2(2):213-219
A necessary and sufficient condition for the correct formulation of boundary integral equations of harmonic functions is established in the present paper. A super-determined problem of harmonic functions is proposed for the first time. Then a necessary and sufficient condition for the existence of solution of the super-determined problem is proved. At the same time, it is a necessary and sufficient condition for the correct formulation of boundary integral equations with direct unknown quantities. A relation between boundary integral equations and variational principles is discovered for the first time. And a one-to-one correspondence between boundary integral equations with direct and indirect unknown quantities is indicated. The concept and route of the present paper can be applied to other boundary value problems possessing variational principles. 相似文献
18.
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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P. H. Wen M. H. Aliabadi D. P. Rooke 《Archive of Applied Mechanics (Ingenieur Archiv)》1996,66(5):326-335
Summary In this paper, an indirect boundary integral equation method for the solution of dynamic crack problems is presented. The Laplace transform method is used to derive the fundamental solutions for the opening mode (mode I) and the sliding mode (mode II) displacement discontinuity. Accurate dynamic stress intensity factorsK
N
(t) (N=I,II) resulting from different time-dependent loads on the crack surface are obtained. The specific influences of the various elastic waves on the stress intensity factors can be clearly seen from the results.On leave Central-South University of Technology Changsha, P.R. China 相似文献