共查询到19条相似文献,搜索用时 921 毫秒
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提出了间接求解传统Helmholtz边界积分方程CBIE的强奇异积分和自由项系数,以及Burton-Miller边界积分方程BMBIE中的超强奇异积分的特解法。对于声场的内域问题,给出了满足Helmholtz控制方程的特解,间接求出了CBIE中的强奇异积分和自由项系数。对于声场外域对应的BMBIE中的超强奇异积分,按Guiggiani方法计算其柯西主值积分需要进行泰勒级数展开的高阶近似,公式繁复,实施困难。本文给出了满足Helmholtz控制方程和Sommerfeld散射条件的特解,提出了间接求出超强奇异积分的方法。推导了轴对称结构外场问题的强奇异积分中的柯西主值积分表达式,并通过轴对称问题算例证明了本文方法的高效性。数值结果表明,对于内域问题,采用本文特解法的计算结果优于直接求解强奇异积分和自由项系数的结果,且本文的特解法可避免针对具体几何信息计算自由项系数,因而具有更好的适用性。对于外域问题,两者精度相当,但本文的特解法可避免对核函数进行高阶泰勒级数展开,更易于数值实施。 相似文献
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本文讨论了r~1型及lnr型二维域奇异积分的解析计算。对多项式荷载给出了域奇异积分的正确公式。而对于一般荷载,利用泰勒展开化为多项式荷载进行积分,并给出了积分误差估计。计算结果表明,本文方法是有效的。 相似文献
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非连续边界元积分的精确表达式及相关问题 总被引:5,自引:0,他引:5
以二维位势问题边界元分析为例,给出了利用线性非连续边界元离散边界积分方程时系数矩阵积分计算的精确表达式,通过和利用Gauss积分方法计算系数矩阵所得数值结果的比较表明:配位点选择不同对数值计算结果精度影响的主要原因是积分计算的精度,尤其当配位因子选择较大时,存在的准奇异积分(Nearly Singular Integrals)很难利用常规Gauss积分方法准确求得。 相似文献
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对线弹性平面问题的边界轮廓法,选用完备的二次位移形函数,使求问题的维数降低两维,给出了求解边界位移和面力以及内点应力的求解方法。证明平面弹怀断鲜明力学Ja积分、M积分、L积分方程的被积函数的散度均等于零,将它们分别转化为边界点的位移和面力的线性迭加,无需计算数值积分,算例表明,本文方法具有较高的精度。 相似文献
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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
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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
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Three-dimensional edge cracks are analyzed using the Self-Similar Crack Expansion (SSCE) method with a boundary integral equation
technique. The boundary integral equations for surface cracks in a half space are presented based on a half space Green's
function (Mindlin, 1936). By using the SSCE method, the stress intensity factors are determined by the crack-opening displacement
over the crack surface. In discrete boundary integral equations, the regular and singular integrals on the crack surface elements
are evaluated by an analytical method, and the closed form expressions of the integrals are given for subsurface cracks and
edge crakcs. This globally numerical and locally analytical method improves the solution accuracy and computational effort.
Numerical results for edge cracks under tensile loading with various geometries, such as rectangular cracks, elliptical cracks,
and semi-circular cracks, are presented using the SSCE method. Results for stress intensity factors of those surface breaking
cracks are in good agreement with other numerical and analytical solutions. 相似文献
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提出了一种精确计算任意高阶奇异曲线积分的直接计算法.首先将曲线单元上的各种几何量用投影线上的几何量来表示,然后通过幂级数展开和解析的方法显式地消除了积分的奇异性.还导出了计算等参坐标对局部直角坐标偏导数的表达式.由于这种方法涉及到的是总体尺度间的坐标变换,操作起来直观明了,可以处理二维问题边界元分析中出现的任意高阶奇异边界积分.最后用具体算例验证该方法的正确性. 相似文献
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王左辉 《应用数学和力学(英文版)》1993,14(8):767-776
In this paper,the nonsingular fundamental solutions are obtained from Fourierseries under some given conditions.These solutions can be taken as the kernels ofintegral equation.So a new boundary element method is presented,with which allkinds of thin-plate bending problems can’be solved,even with complicated loadings andsinuous boundaries.The calculation is much simpler and more accurate. 相似文献
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选择二次完全多项多作为位移形函数,对边界轮廓法作了进一步的发展,证明二维弹性断裂问题的J积分方程的被积分函数的散度等于零,将J积分化为边界点的势函数数值的计算,无需计算数值积分,算例表明,该方法较传统边界元法求得的结果精度更好。 相似文献
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This paper applies a Hamiltonian method to study analytically the stress dis- tributions of orthotropic two-dimensional elasticity in(x,z)plane for arbitrary boundary conditions without beam assumptions.It is a method of separable variables for partial differential equations using displacements and their conjugate stresses as unknowns.Since coordinates(x,z)can not be easily separated,an alternative symplectic expansion is used. Similar to the Hamiltonian formulation in classical dynamics,we treat the x coordinate as time variable so that z becomes the only independent coordinate in the Hamiltonian ma- trix differential operator.The exponential of the Hamiltonian matrix is symplectic.There are homogenous solutions with constants to be determined by the boundary conditions and particular integrals satisfying the loading conditions.The homogenous solutions consist of the eigen-solutions of the derogatory zero eigenvalues(zero eigen-solutions) and that of the well-behaved nonzero eigenvalues(nonzero eigen-solutions).The Jordan chains at zero eigenvalues give the classical Saint-Venant solutions associated with aver- aged global behaviors such as rigid-body translation,rigid-body rotation or bending.On the other hand,the nonzero eigen-solutions describe the exponentially decaying localized solutions usually ignored by Saint-Venant's principle.Completed numerical examples are newly given to compare with established results. 相似文献
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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