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1.
由于Helmholtz方程的基本解是频率的函数,因此传统边界元法在处理声场特征值问题时具有天生的缺陷。本文采用Laplace方程基本解生成积分方程,通过径向积分法将在此过程中产生的域积分项转化为边界积分。此方法克服了传统边界元法系数矩阵对频率的依赖,同时克服了特解积分法对特解的依赖,并通过对表面声导纳的多项式逼近,将敷设多孔吸声材料声腔特征值问题转化为矩阵多项式,从而避免了复杂的非线性求解。通过数值算例验证了算法的有效性。  相似文献   

2.
A new numerical method—Green quasifunction is proposed.The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation,a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome.Finally,natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method.  相似文献   

3.
有限散射信号下二维缺陷形状识别的罚函数方法   总被引:1,自引:0,他引:1  
冯文杰  邹振祝 《力学学报》2001,33(4):499-507
研究在有限照射角度和频带宽度下二维缺陷的形状识别问题。首先,通过引进介质参数扰动函数,建立介质参数扰动函数和弹性波散射场之间的非线性关系,并将所关心的缺陷的形状识别问题转化为关于扰动函数的反演;然后,利用变分技术和优化方法求解,为了弥补散射数据的不足,在总的目标函数中,采用附加度量函数作为罚函数;最后,对后场散射远场测量时有限照射角度和频带宽度下几种典型缺陷进行了模拟识别,表明了;表明了罚函数法的有效性。  相似文献   

4.
The solution of a dynamic problem for calculation of a displacement field on a half-space surface caused by an internal mode I crack opening is presented. The problem is reduced to the system of boundary integral equations (BIEs). The equations of motion are solved with the use of Helmholtz potentials and applying Fourier integral transform. The effects of the crack size, the crack depth and the distance from the crack epicenter to the observation point on the parameters of elastic waves are investigated. It is established that the increasing of the defect size leads to narrowing bandwidth of elastic waves and to lowering of center frequency. The analysis given here can be used for identification of the crack growth during technical diagnostic of an industry objects and structural elements by AE method.  相似文献   

5.
The hyper-singular boundary integral equation method of crack analysis in three-dimensional transversely isotropic magnetoelectroelastic media is proposed. Based on the fundamental solutions or Green’s functions of three-dimensional transversely isotropic magnetoelectroelastic media and the corresponding Somigliana identity, the boundary integral equations for a planar crack of arbitrary shape in the plane of isotropy are obtained in terms of the extended displacement discontinuities across crack faces. The extended displacement discontinuities include the displacement discontinuities, the electric potential discontinuity and the magnetic potential discontinuity, and correspondingly the extended tractions on crack face represent the conventional tractions, the electric displacement and the magnetic induction boundary values. The near crack tip fields and the intensity factors in terms of the extended displacement discontinuities are derived by boundary integral equation approach. A solution method is proposed by use of the analogy between the boundary integral equations of the magnetoelectroelastic media and the purely elastic materials. The influence of different electric and magnetic boundary conditions, i.e., electrically and magnetically impermeable and permeable conditions, electrically impermeable and magnetically permeable condition, and electrically permeable and magnetically impermeable condition, on the solutions is studied. The crack opening model is proposed to consider the real crack opening and the electric and magnetic fields in the crack cavity under combined mechanical-electric-magnetic loadings. An iteration approach is presented for the solution of the non-linear model. The exact solution is obtained for the case of uniformly applied loadings on the crack faces. Numerical results for a square crack under different electric and magnetic boundary conditions are displayed to demonstrate the proposed method.  相似文献   

6.
Boundary integral equations and boundary element methods were employed analytically, semi-analytically and numerically to study the occurrence of fictitious frequency for the exterior Helmholtz equations subject to the mixed-type boundary conditions. A semi-infinite rod and a circular radiator of problems were addressed. Degenerate kernel of the fundamental solution and Fourier series for boundary density were utilized in the null-field integral equation to examine the occurrence of fictitious frequency semi-analytically. The BEM was utilized to solve the solution numerically. The CHIEF technique and Burton and Miller method were adopted to suppress the occurrence of the fictitious frequency. It is emphasized that the occurrence of fictitious frequency depend on the adopted method (singular or hypersingular formulation) no matter what the given type of boundary condition for the problem is. The illustrative examples were tested to verify this finding successfully.  相似文献   

7.
本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,本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,本文算法稳定、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   

8.
三维变系数热传导问题边界元分析中几乎奇异积分计算   总被引:2,自引:2,他引:0  
在边界积分的数值计算过程中,当源点离积分单元很近时,边界积分就会具有几乎奇异性,此时不能直接用高斯数值积分公式计算几乎奇异积分。本文以三维非均质热传导问题为例,介绍了一种计算几乎奇异边界积分的新方法。首先,采用Newton-Raphson迭代算法确定积分单元上离源点最近的点;然后,将积分单元上任意一点的坐标在最近点处展开成泰勒级数,并计算源点到积分单元任意点的距离;最后,将距离函数代入几乎奇异边界积分中,并运用指数变换方法导出积分单元上几乎奇异积分的计算公式。文中给出了两个非均质热传导问题的算例来验证所述方法的正确性、有效性和稳定性。  相似文献   

9.
Direct and inverse problems of forced antiplane vibrations of a transverse inhomogeneous elastic layer are considered. The mechanical characteristics of the layer (density and shear modulus) are considered to be functions of the transverse coordinate. A method for solving the direct problem, based on using the integral Fourier transform and solving the boundary problem by the shooting method, is proposed. The inverse problem of determining the distributions of the mechanical parameters based on the known information on the wave field on some part of the upper surface is considered. Iterative sequences of integral equations are constructed. Results of numerical experiments and recommendations on the optimal choice of the vibration frequency and the interval, on which the displacements are determined, are given.  相似文献   

10.
The idea of quasi-Green's function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi- Green's function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob- lem. The mode shape differential equations of the free vibration problem of a simply- supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa- tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green's function method.  相似文献   

11.
近场波动模拟的一种应力人工边界   总被引:29,自引:1,他引:28  
采用平面波和远场散射波混合透射,引入无限介质线弹性本构关系建立了一种应力人工 边界条件. 其优点在于边界结点反应与内部有限元结点反应采用相同的积分格式计算,有限 元积分方法稳定时不存在人工边界失稳问题. 数值算例表明:边界精度高于现有黏性边 界、黏弹性人工边界,以及一、二阶透射人工边界.  相似文献   

12.
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   

13.
The idea of Green quasifunction method is clarified in detail by considering a free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation, the irregularity of the kernel of integral equations is avoided.Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method.  相似文献   

14.
通过间解的分离,本文将径向多裂纹柱体的导曲函两个调和函数表示,使问题归为解一组混混合型积分方程。针对方程的特点,本文联合使用三次样条边界法与奇异积分方程的数值方法对所得方程建立了数值法,并对裂纹相交情形作了特殊处理。最后对工程中感兴趣的一些典型的多裂纹柱体的扭转作了例题计算,结果表明,本文方法具有收敛快,精度高的特点。  相似文献   

15.
16.
加权残数配点法解正交各向异性板的积分方程   总被引:1,自引:0,他引:1  
本文推导了一般各向异性板弯曲的积分方程,运用加权残数配点法求解了正交各向异性板弯曲的积发方程,本文将部分配点取在边界上,另一部分配点取在域外,只用关于找度的基本积分方程,而不用关于转角的补充积分方程,简化了方程求解和计算程序,由于正交各向异性板没有争析形式的、实用的基本解,本文提出了两种新的近似基本解;加权双三角级数;广义各向同性板解析形式的基本解和加权双三角级数的叠加,算例表明,本文提出的解法和近似基本解适用于各类边界条件的正交各向异性板,具有简单、可靠、精度高等优点。  相似文献   

17.
利用边界元法求解瞬态弹性动力学问题时,时域基本解函数的分段连续性和奇异性为该问题的求解带来很大的困难。为了解决时域基本解中的奇异性问题,本文依据柯西主值的定义,对经过时间解析积分之后的时域基本解进行奇异值分解,将其分成奇异和正则积分两部分;其中正则部分可通过采用常规高斯积分方法来计算,而奇异部分具有简单的形式,可以利用解析积分计算。经过上述操作之后,就可以达到直接消除时域基本解中奇异积分的目的。和传统方法相比,本文方法并不依赖静力学基本解来消除奇异性,是一种直接求解方法。最后给定两个数值算例来验证本文提出方法的正确性和可行性,结果表明使用本文算法可以解决弹性动力学边界积分方程中的奇异性问题。  相似文献   

18.
Based on linearized 2-D Navier-Stokes equation, a Laplace transform-boundary element coupling method for viscous fluid-structure impact analysis is proposed. Under assumption of incompressibility for the fluid, the corresponding equivalent boundary integral equation in terms of the potential function and stream function is first established by Lamb's transform in the Laplace transform domain. It enables us to solve impact water problems in frequency domain by the boundary element method, in which the effect of viscous flow on the dynamic response can be taken into account. Then a complete solution of the problem under consideration in time domain is obtained by means of Durbin's formulas for the numerical inversion of the Laplace transform. Finally, a practical example is given to confirm the validity of the present method. Project supported by the National Defence Foundation of Science & Technology of China (No. J14. 8. 1. JW0515).  相似文献   

19.
利用固定网格法分析三维非稳定渗流问题时,将要面对两项积分难题:以自由面及单元表面为边界的空间积分及以自由面为边界的曲面积分。针对常用的任意8结点6平面三维普通单元,提出采用坐标变换及等参变换技术求取空间积分项的精确数值解;至于曲面积分项,建议改用单元非饱和区部分表面作为积分边界,经过坐标变换及等参变换处理积分边界后,利用高斯数值积分可求出曲面积分项的精确数值解。通过一个普通单元及一项均质半无限边界堤坝的实例分析,表明此方法的精确性和稳定性良好。  相似文献   

20.
依据弹性力学虚边界元法的基本思想和电磁弹性固体的基本解,提出了电磁弹性固体三维问题的虚边界元-等额配点法.该方法继承传统边界元法优点的同时,有效地避免了传统边界元法的边界积分奇异性的问题.算例表明该方法有很高的精度,是求解电磁弹性固体三维问题的一个有效的数值方法.  相似文献   

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