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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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数值求解不可压粘性流体定常运动的格林函数方法 总被引:3,自引:0,他引:3
本文提出了一种数值求解不可压粘性流体定常运动的格林函数方法.在本文中利用Stokes方程的基本解作为格林函数将求解不可压粘性流体定常运动的边值问题化为求解速度场和边界应力的非线性积分方程组,在解出速度场和边界应力后可直接计算流场中各点的压力;用有限元近似将积分方程离散化而进行数值求解。对于小雷诺数流动,只归结为求解边界积分方程,使求解区域减少一个维度。对于非线性问题,可用迭代方法求解,在每次迭代中只须解出边界点上的速度或应力。通过几个简单的算例,表明本文所提出的方法具有精度高、处理边界条件简单、通用性强的优点,并具有求解各种复杂流动的潜力。 相似文献
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文中提出用边界积分方程法解具有自由边界的粘滞不可压缩流问题。Navier—Stokes方程中的非线性项是通过线性化近似求解的。作为对这种方法的检验,计算了失重情况下容器内粘滞流体因表面张力变化(由温差引起)而产生的旋流,并将计算结果与用有限差分法所得结果作了比较。此外,还初步计算了在管内压力作用下液滴的形成过程。 相似文献
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采用格林公式和基本解推导出直接边界积分方程来求解渗流问题.边界积分方程数值离散基于格林元方法(Green element methond),改进了原方法中压力和压力导数的求解方法,命名为混合边界元方法(Mixed boundary element method).相较于格林元类方法,该方法显式考虑了求解节点的外法向流量值和压力值,并使求得的数值解在求解区域上能够连续,符合实际的物理过程,在不增加额外未知数的情况下提高了计算精度.分析了不同网格类型对模拟计算结果的影响,并对稳定渗流问题、非稳定(瞬态)渗流问题和非稳态问题进行了实例计算,结果显示改进方法提高了计算精度,并对各类渗流问题有较好的适应性. 相似文献
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边界积分方程—边界元法的基本理论及其在弹性力学方面的若干工程应用 总被引:2,自引:0,他引:2
本文第一部分对于直接法弹性力学边界积分方程的基本理论作了论述,全文采用内积公式以加权余量形式来建立边界积分方程.论述范围包括位势问题、弹性静力学问题和克希霍夫型平板理论的边界积分方程—边界元法.文中同时写出相应的变分格式.并讨论了非光滑边界的处理.本文第二部分简介对若干具体问题用特定的基本解进行的有关数值计算.文中介绍的研究组所获初步结果包括:迴转体的扭转、轴对称问题和弯曲问题,以及平板弯曲问题的边界积分方程—边界元法应用的具体结果.计算结果表明对于改进和扩充工程实用应力集中数据及平板计算(包括自由边界及角点问题)将是有益的. 相似文献
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本文提出了一个用边界积分方程——边界元法解克希霍夫平板弯曲问题的协调方案.这个方案在边界上的协调程度与一般有限元法的协调板单元方案相当. 文中给出了边界积分方程的建立方法及有关公式,叙述了数值解的有关过程,对几种角度的悬臂三角板进行了计算.计算结果表明:此方案具有较高的精度,在达到同样精度的前提下可以降低计算成本,所以它对于改进与补充平板计算的数值方法是有益的. 相似文献
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《Journal of Fluids and Structures》2002,16(1):71-82
In the present paper, a general integral equation is presented to calculate the forces exerted on a two-dimensional (2-D) body of arbitrary shape immersed in unsteady, incompressible flows. By finding the general solutions of a set of Laplace equations with particular boundary conditions, the equation can be simplified to produce a simplified formula for calculating the forces. The simplified formula consists of three parts, representing contributions from different physical phenomena: added mass force and/or inertial force in inviscid flow, the force caused by the deformation of fluid and viscosity and the force caused by the convection of fluid with nonzero circulation. It can be applied to any 2-D arbitrary body in viscous or inviscid, steady or unsteady incompressible flow. As the formula excludes either temporal derivatives of velocity or spatial derivatives of vorticity in the flow field, the numerical errors contained in the numerical solution of velocity and vorticity fields will not be magnified, and therefore the resulting force calculated is more accurate. Most importantly, the formula presents an alternative method for obtaining the added mass of a 2-D body of arbitrary shape accelerating in a fluid. For bodies of simple shape, such as a circle, ellipse and plate, the added masses predicted using the present method are in agreement with that obtained by conventional methods. For bodies of complex shape, the present method only requires the calculation of the first two coefficients of the conformal transformation and cross-sectional area. 相似文献
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IntroductionConcerningtheelasticplaneprobleminaunitcircle ,ZhengShenzhouandZhengXueliangdevelopedaboundaryintegralformulaofthestressfunction[1]:Φ(r,θ) =-( 1 -r2 ) 24π ∫2π0ν( φ)1 -2rcos(θ-φ) r2 dφ 12π∫2π011 -2rcos(θ-ω) r2 dω∫2π0μ( φ)1 -cos(ω-φ) dφ 1 -r22π∫2π0μ( φ)1 -2rcos(θ -φ) r2 dφ ( 0 ≤r <1 ) ,( 1 )whereμ(θ) =Φ(r,θ) |r=1,ν(θ) = Φ n r=1= Φ r r=1.Intheformula ( 1 )theseconditemisastrongsingularintegral,itshouldbeunderstoodasanintegra… 相似文献
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An approximate method on the conformal mapping from a unit circle to an arbitrary curve 总被引:3,自引:0,他引:3
郑志强 《应用数学和力学(英文版)》1992,13(5):467-475
In this paper, the conformal mapping problem on the transformation from the interior of a unit circle to the interior of the simply connected region or exterior with an arbitrary curvilinear boundary (including an arbitrary curvilinear cut crack) is discussed. The boundary of the simply connected region is approximated by a polygon. The mapping function from a unit circle to a polygon is founded by using the Schwartz-Christoffel integral. A numerical calculation method to determine the unknown parameters in the Schwartz-Christoffel integral is given. 相似文献
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Yung-Chao Wu 《国际流体数值方法杂志》1988,8(7):803-811
This paper describes the characteristics of small-amplitude waves generated by a sinusoidally oscillating, inclined paddle-type wavemaker operating in a constant-depth channel. Two-dimensional, linearized potential flow is assumed. A semi-analytical method, the boundary collocation method, is used to establish the relationship between wave amplitude and paddle stroke. The numerical results are compared with the numerical results of the boundary integral equation method. It is found that the boundary collocation method is simpler and more flexible to implement and faster to compute. In addition, the numerical results are in reasonably good agreement with the laboratory experimental data. For the vertical wavemaker, which is a special case of the inclined wavemaker, an analytical series solution can be found. By using the boundary collocation method and the boundary integral equation method to solve the vertical wavemaker problem and comparing the results with the analytical series solution, it is found that the boundary collocation method yields a solution which is much more accurate than that from the boundary integral equation method. Finally, the relationships between wave amplitude and paddle stroke are established for different inclinations of the paddle-type wavemaker, based on the boundary collocation method. 相似文献
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《Wave Motion》2017
Aeroacoustic scattering prediction generally relies on boundary integral methods which require evaluation of the impermeability condition on the scattering surface. The boundary condition implies zero normal velocity relative to the scattering surface. This condition has been expressed by relating the acoustic velocity to the acoustic pressure gradient, allowing indirect evaluation of the boundary condition by existent acoustic pressure gradient formulations. In the present paper, a direct evaluation of the hardwall boundary condition in scattering problems is demonstrated by time-domain analytic acoustic velocity formulae. Acoustic velocity formulations V1A and KV1A are implemented for acoustic scattering prediction, by hybrid approaches based on the FW–H equation and the Kirchhoff method These formulations can be coupled to any scattering solver, allowing time-domain prediction of the incident acoustic field when broadband noise generation is concerned. Formulation V1A offers mathematical simplicity and computational efficiency, which can be advantageous for realistic scattering applications. Implementation of formula KV1A enables acoustic scattering prediction by existing solvers based on the Kirchhoff method. The validity of the suggested methodology is assessed through the analytical test case of harmonic sound scattered by a rigid sphere. Sound propagation and scattering effects are analyzed by examination of the acoustic velocity field characteristics. 相似文献
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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
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A simple technique is presented that allows a numerical solution to be sought for the vertical variation of shear stress as a substitute for the vertical variation of velocity in a three-dimensional hydrodynamic model. In its most general form the direct stress solution (DSS) method depends only upon the validity of an eddy viscosity relation between the shear stress and the vertical gradient of velocity. The rationale for preferring a numerical solution for shear stress to one for velocity is that shear stress tends to vary more slowly over the vertical than velocity, particularly near boundaries. Consequently, a numerical solution can be obtained much more efficiently for shear stress than for velocity. When needed, the velocity profile can be recovered from the stress profile by solving a one-dimensional integral equation over the vertical. For most practical problems this equation can be solved in closed form. Comparisons are presented between the DSS technique, the standard velocity solution technique and analytical solutions for wind-driven circulation in an unstratified, closed, rectangular channel governed by the linear equations of motion. In no case was the computational effort required by the velocity solution competitive with the DSS when a physically realistic boundary layer was included. The DSS technique should be particularly beneficial in numerical models of relatively shallow water bodies in which the bottom and surface boundary layers occupy a significant portion of the water column. 相似文献
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本文利用Green第二公式,将Reynolds方程转化为沿边界的积分方程,并将非线性项作为自由项的一部分处理,采用常单元离散边界Γ,用迭代技术求出油膜压力分布,与有限差分法和有限元法比较,边界元法的结果更接近解析解. 相似文献
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Dr. T. Zlatanovski 《Archive of Applied Mechanics (Ingenieur Archiv)》1995,65(5):346-364
Summary A boundary integral equation method is proposed for approximate numerical and exact analytical solutions to fully developed incompressible laminar flow in straight ducts of multiply or simply connected cross-section. It is based on a direct reduction of the problem to the solution of a singular integral equation for the vorticity field in the cross section of the duct. For the numerical solution of the singular integral equation, a simple discretization of it along the cross-section boundary is used. It leads to satisfactory rapid convergency and to accurate results. The concept of hydrodynamic moment of inertia is introduced in order to easily calculate the flow rate, the main velocity, and the fRe-factor. As an example, the exact analytical and, comparatively, the approximate numerical solution of the problem of a circular pipe with two circular rods are presented. In the literature, this is the first non-trivial exact analytical solution of the problem for triply connected cross section domains. The solution to the Saint-Venant torsion problem, as a special case of the laminar duct-flow problem, is herein entirely incorporated. 相似文献