共查询到19条相似文献,搜索用时 109 毫秒
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含曲线裂纹圆柱扭转问题的新边界元法 总被引:4,自引:0,他引:4
研究含曲线裂纹圆柱的Saint-Venant扭转,将问题化归为裂纹上边界积分方程的求解.利用裂纹尖端的奇异元和线性元插值模型,给出了扭转刚度和应力强度因子的边界元计算公式.对圆弧裂纹、曲折裂纹以及直线裂纹的典型问题进行了数值计算,并与用Gauss-Chebyshev求积法计算的直裂纹情形结果进行了比较,证明了方法的有效性和正确性. 相似文献
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在局部边界积分方程方法中,当源节点位于分析域的整体边界上时,局部边界积分将出现奇异积分问题,这些奇异积分需要做特别的处理.为此,提出了对域内节点采用局部积分方程,而对边界节点直接采用移动最小二乘近似函数引入边界条件来解决奇异积分问题,这同时也解决了对积分边界进行插值引入近似误差的问题.作为应用和数值实验,对Laplace方程和Helmholtz方程问题进行了分析,取得了很好的数值结果.进而,在Helmholtz方程求解中,采用了含波解信息的修正基函数来代替单项式基函数进行近似.数值结果显示,这样处理是简单高效的,在高波数声传播问题的求解中非常具有前景. 相似文献
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非对称载荷作用的外部圆形裂纹问题 总被引:2,自引:2,他引:0
使用边界积分方程方法,研究了三维无限弹性体中受非对称载荷作用的外部圆形裂纹问题。通过使用Fourier级数和超几何函数,将问题的二维边界奇异积分方程简化为Abel型方程,获得了一般非对称载荷作用的外部圆形裂纹问题的应力强度因子精确解,比用Hankel变换法得到的结果更为一般。结果表明:边界积分方程法在解析分析方面还有很大的潜力。 相似文献
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三维瞬态弹性动力场的基本解及边界积分方程 总被引:1,自引:0,他引:1
三维瞬态动力场的求解,一直为世人所瞩目,本文拟采用边界积分方程——边界单元法进行求解。与其它数值方法相比较,本方法由于采用了动力场区域的基本解,因此在处理无限域或半无限域的动力场问题时可以毋须人为地去划定边界,附加相应的边界约束条件。同时在求解过程中,采用了权函数与奇异格林函数,使得域积分可以转化为边界积 相似文献
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该文研究了光滑区域上二维Helmholtz方程阻尼边界条件外问题的数值解法, 应用单双层位势组合来逼近散射场, 因此积分方程中含有超奇异算子. 给出了超奇异算子的离散化方法, 在Holder空间中给出了误差估计和解析边界的收敛性分析. 最后针对该方法给出数值实例, 以表明该方法的有效性. 相似文献
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针对多裂纹问题,若采用常规的数值求解技术,计算效率较低.为实现多裂纹问题的大规模数值模拟,建立了本征裂纹张开位移(crack opening displacement, COD)边界积分方程及其迭代算法,并引入Eshelby矩阵的定义,将多裂纹分为近场裂纹和远场裂纹来处理裂纹间的相互影响.以采用常单元作为离散单元的快速多极边界元法为参照,对提出的计算模型和迭代算法进行了数值验证.结果表明,本征COD边界积分方程方法在处理多裂纹问题时取得较大的改进,其计算效率显著高于传统的边界元法和快速多极边界元法. 相似文献
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《Mathematical and Computer Modelling》2006,43(1-2):76-88
The dual reciprocity boundary element method employing the step by step time integration technique is developed to analyse two-dimensional dynamic crack problems. In this method the equation of motion is expressed in boundary integral form using elastostatic fundamental solutions. In order to transform the domain integral into an equivalent boundary integral, a general radial basis function is used for the derivation of the particular solutions. The dual reciprocity boundary element method is combined with an efficient subregion boundary element method to overcome the difficulty of a singular system of algebraic equations in crack problems. Dynamic stress intensity factors are calculated using the discontinuous quarter-point elements. Several examples are presented to show the formulation details and to demonstrate the computational efficiency of the method. 相似文献
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This work presents a time-domain hypersingular integral equation (TD-HIE) method for modeling 3D crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites (EMTE-CVP-MCs) under extended incremental loads rate through intricate theoretical analysis and numerical simulations. Using Green’s functions, the extended general incremental displacement rate solutions are obtained by time-domain boundary element method. Three-dimensional arbitrary crack growth problem in EMTE-CVP-MCs is reduced to solving a set of TD-HIEs coupled with boundary integral equations, in which the unknown functions are the extended incremental displacement discontinuities gradient. Then, the behavior of the extended incremental displacement discontinuities gradient around the crack front terminating at the interface is analyzed by the time-domain main-part analysis method of TD-HIE. Also, analytical solutions of the extended singular incremental stresses gradient and extended incremental integral near the crack fronts in EMTE-CVP-MCs are provided. In addition, a numerical method of the TD-HIE for a 3D crack subjected to extended incremental loads rate is put forward with the extended incremental displacement discontinuities gradient approximated by the product of time-domain basic density functions and polynomials. Finally, examples are presented to demonstrate the application of the proposed method. 相似文献
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An extended displacement discontinuity (EDD) boundary integral equation method is proposed for analysis of arbitrarily shaped planar cracks in two-dimensional (2D) hexagonal quasicrystals (QCs) with thermal effects. The EDDs include the phonon and phason displacement discontinuities and the temperature discontinuity on the crack surface. Green's functions for unit point EDDs in an infinite three-dimensional medium of 2D hexagonal QC are derived using the Hankel transform method. Based on the Green's functions and the superposition theorem, the EDD boundary integral equations for an arbitrarily shaped planar crack in an infinite 2D hexagonal QC body are established. Using the EDD boundary integral equation method, the asymptotic behavior along the crack front is studied and the classical singular index of 1/2 is obtained at the crack edge. The extended stress intensity factors are expressed in terms of the EDDs across crack surfaces. Finally, the energy release rate is obtained using the definitions of the stress intensity factors. 相似文献
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By using the method of generalized conjugation problems, we propose a numerical scheme for investigation of the redistribution of temperature stresses in a piecewise-homogeneous cylindrical shell caused by a longitudinal crack. This scheme is based on systems of integral equations (some of them are singular) to determine the unknown jumps of integral characteristics of the disturbed temperature field and displacements and their derivatives on the line of a crack and on the interface as well as the derivatives of these integral characteristics with respect to the longitudinal coordinate at the interface. 相似文献
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Steen Krenk 《Integral Equations and Operator Theory》1982,5(1):548-561
The dominant part of an integral equation arising in connection with boundary value problems for the circular disc is evaluated in terms of orthogonal polynomials. This relation leads to an efficient method for numerical solution of the complete integral equation even in the presence of a complicated bounded kernel. The static problem of a circular crack in an infinite elastic body under general loads is used to illustrate vector boundary conditions leading to two coupled integral equations, while the problem of a vibrating flexible circular plate in frictionless contact with an elastic half space is solved by use of the associated numerical method. 相似文献
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Arvet Pedas Enn Tamme 《Applied Numerical Mathematics》2011,61(6):738-751
A fully discrete version of a piecewise polynomial collocation method is constructed to solve initial or boundary value problems of linear Fredholm integro-differential equations with weakly singular kernels. Using an integral equation reformulation and special graded grids, optimal global convergence estimates are derived. For special values of parameters an improvement of the convergence rate of elaborated numerical schemes is established. Some of our theoretical results are illustrated by numerical experiments. 相似文献
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A new boundary integral equation formulation for solving plane elasticity problems involving orthotropic media is presented in this paper. Based on the real variable fundamental solutions of the considered problems, a limit theorem for the transformation from domain integral equations into boundary integral equations (BIEs) and a novel decomposition technique to the fundamental solutions, the regularized BIEs with indirect unknowns, which do not involve the direct calculation of CPV and HFP integrals, are established. The limiting process is done in global coordinates and no separate numerical treatment for strong and weak singular integrals was necessary. The current method does not need to transform the considered problems into isotropic ones as is normally done in the existing literature, so no inverse transform is required. The numerical implementation is carried out using both discontinuous quadratic elements and exact elements, which is developed to model its boundary with negligible error. The validity of the proposed scheme is demonstrated by three numerical examples. Excellent agreement between the numerical results and exact solutions was obtained even with using small amounts of element. 相似文献