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将重构核粒子法和势问题的边界积分方程方法结合,提出了势问题的重构核粒子边界无单元
法. 推导了势问题的重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核
粒子边界无单元法的离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位势的
积分公式. 重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点
的精确值,所以该方法具有更高的精度. 最后给出了数值算例,验证了所提方法的有效性
和正确性. } 相似文献
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本文针对各向异性势问题提出了一类充分必要的随机边界积分方程,数值计算结果表明在退化尺度附近,充要的随机边界积分程较习用的随机边界积分方程有较大的优越性。 相似文献
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水平均流中细管排放气泡的三维数值模拟 总被引:3,自引:0,他引:3
在液体为无粘不可压,流动有势和气体遵循完全气体绝热关系的假定下,本文应用边界积分方程方法数值模拟了水平均流中垂直细管排放气泡的三维动力学问题,边界采用高阶有限元表达。文中介绍了有关泡面法向矢量、切向速度、曲率和接触线等的计算技术。与已知解的比较,表明了这一数值方法的高精度和优越性。算例显示了水平均流对于气泡形状和体积的影响 相似文献
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非连续边界元——有限元耦合方法分析 总被引:4,自引:0,他引:4
对边界元-有限元耦合方法进行了分析,采用非连续元离散边界积分方程,解决了耦合分析中自由度约束问题,给出了非连续边界元同有限元耦合的具体实施步骤,通过对二维弹性力学和流=固耦合问题分析,表明了该文方法的有效性。 相似文献
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缓变主流中三维气泡的非线性振动 总被引:1,自引:0,他引:1
空化现象和水下噪声机制与液体中气泡的动力学行为密切相关.在无粘势流的假定下,采用多参数摄动分析,研究了缓变主流中三维气泡的非线性体积模态振动.推导了关于缓变泡形展开的各阶扰动方程,获得了一阶振动的演化方程和一些特殊情况下的解析解;并采用高阶有限元离散的边界积分方程方法,对平面固壁和自由面附近三维气泡的固有频率进行了数值计算 相似文献
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将平面弹性力学确定性的充分必要的边界积分方程推广到含材料常数随机的不确定问题中去,给出了位移的均值以及偏差的充分必要的边界积分方程。数值计算结果表明,和确定性的积分方程一样,习用的随机边界积分方程在退化尺度附近,无论是均值还是偏差都存在巨大的误差,而充要的随机边界积分方程则始终保持良好的精度 相似文献
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Huang Yuying Yue Dongyi Qian Qin 《Acta Mechanica Solida Sinica》1995,8(4):337-348
A reciprocal theorem of dynamics for potential flow problems is first derived by meansof the Laplace transform in which the compressibility of water is taken into account.Based on this the-orem,the corresponding time-space boundary integral equation is obtained.Then,a set of time do-main boundary element equations with recurrence form is immediately formulated through discretiza-tion in both time and boundary.After having carried out the numerical calculation two solutions arefound in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impacton the surface of a half-space fluid.The results show that the present method is more efficient than theprevious ones. 相似文献
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The problem of time minimization of a holonomic scleronomic mechanical system on a prescribed trajectory between two specified
positions in configuration space is solved. The generalized force with restricted coordinates is taken as the controlling
force. The application of the Green theorem (the well-known Miele method in flight mechanics) has shown that at every instant
at least one control is at its boundary and possesses controlling functions with interruptions. It is assumed that at least
one generalized coordinate exists that is monotonous during the interval of movement. An algorithm for numerical computation
is presented for assessing the boundary of the admissible domain in the state space, thus, solving the problem of finding
the optimal control as a function of time. Numerical integration is, therefore, carried out forward from the start point and
backward from the end point by the use of the Runge-Kutta method. The mentioned procedure is illustrated in the example of
time minimization for a manipulator which has its tip moving in a straight line. The application of the presented method simplifies
solving of this type of problem compared to other methods, for instance, dynamic programming. 相似文献
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A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given. 相似文献
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N. AkhtarS.K. Sen 《Mechanics Research Communications》2011,38(7):529-531
A theorem for non-axisymmetrical Stokes flow about a shear stress-free plane boundary is established by using a representation for the velocity and pressure fields for the same flow in terms of biharmonic and harmonic functions. A corollary of the theorem is derived which gives the axisymmetrical Stokes flow in terms of the Stokes function about the same boundary. The formulae for drag and torque on the boundary are also given. A few illustrative examples are presented. 相似文献
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H. I. Freedman Shigui Ruan Moxun Tang 《Journal of Dynamics and Differential Equations》1994,6(4):583-600
In this paper, the behavior of a continuous flow in the vicinity of a closed positively invariant subset in a metric space is investigated. The main theorem in this part in some sense generalizes previous results concerning classification of the flow near a compact invariant set in a locally compact metric space which was described by Ura-Kimura (1960) and Bhatia (1969). By applying the obtained main theorem, we are able to prove two persistence theorems. In the first one, several equivalent statements are established, which unify and generalize earlier results based on Liapunov-like functions and those about the equivalence of weak uniform persistence and uniform persistence. The second theorem generalizes the classical uniform persistence theorems based on analysis of the flow on the boundary by relaxing point dissipativity and invariance of the boundary. Several examples are given which show that our theorems will apply to a wider varity of ecological models. 相似文献
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Bao-sheng Zhao Yang Gao Ying-tao Zhao 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(5):605-614
Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan,
a set of necessary conditions on the end-data of axisymmetric circular cylinder in one-dimensional (1D) hexagonal quasicrystals
(QCs) for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state,
and using the reciprocal theorem and general solution, these necessary conditions for the end-data to induce only a decaying
elastostatic state (boundary layer solution) will be translated into appropriate boundary conditions for the circular cylinder
with axisymmetric deformations in 1D hexagonal QCs. The results of the present paper enable us to establish a set of correct
boundary conditions, most of which are obtained for the first time. Furthermore, corresponding necessary conditions for the
case of axisymmetric circular cylinder with transversely isotropic are derived subsequently, and their isotropic elastic counterparts
are also obtained. The accuracy of mixed boundary conditions of isotropic axisymmertic circular cylinder is proved at last. 相似文献
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Fei Ran Tian 《Archive for Rational Mechanics and Analysis》1996,135(2):175-196
In this paper, we study a nonlinear and nonlocal free-boundary dynamics — the Hele-Shaw problem without surface tension when the fluid domain is either bounded or unbounded. The key idea is to use a global quantity, the Cauchy integral of the free boundary, to capture the motion of the boundary. This Cauchy integral is shown to be linear in time. The free boundary at a fixed time is then recovered from its Cauchy integral at that time. The main tool in our analysis isCherednichenko's theorem concerning the inverse properties of the Cauchy integrals.As products of our approach, we establish the short-time existence and uniqueness of classical solutions for analytic initial boundaries. We also show the non-existence of classical solutions for all smooth but non-analytic initial boundaries when there is a sink at either a finite point or at infinity. When the fluid domain is bounded, all solutions except the circular one break down before all the fluid is sucked out from the sink. Regularity results are also obtained when there is a source at a finite point or at infinity. 相似文献
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Fu Bao-lian 《应用数学和力学(英文版)》1984,5(2):1263-1272
This paper gives the modified Castigliano’s theorem, which is more convenient and more extensive for applications than the classical Castigliano’s theorem.The modifications to the classical Castigliano ’s theorem are in following two respects, the first respect is that the expression of the partial derivative with respect to the concentrated load p of the complementary energy density in the clasical Castigliano ’s theorem is replaced by the expressions with teh products of the external loads and influence functions, the modification brings us greatest simplicity and greatest convenience for calculations under various loads; the second respect is that the expressions with the products of the inhomogeneous boundary displacements and the influence functions are introduced into the classical Castigliano’s theorem, the modification provides the theoretical fundamental for solving the problems of various boundary conditions.We show also the method of how to apply the modified Castigliano’s theorem to solve the problems of the surface structural mechanics.Finally, as a calculated example of the applications of the modified Castigliano’s theorem we solved the equation of the deflection surface of the rectangular plate with two adjacent edges built-in and other two adjacent edges free. 相似文献
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Trefftz有限元法(Trefftz finite element method,TFEM)是一种高效的数值计算方法,兼有传统有限元法和边界元法的诸多优点.基于双独立插值模式,结合杂交泛函和高斯散度定理,推得仅含边界积分的有限元格式.简述了过去10年间(2007—2016)Trefftz有限元法在单元域内插值函数、源项处理、特殊功能单元以及非各向同性材料等方面的研究进展,并对未来的发展趋势给出了几点展望. 相似文献
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Christos G. Panagiotopoulos G. D. Manolis 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(12):1429-1447
Reciprocal theorems in elastodynamics are introduced as extensions of respective theorems from elastostatics. Inasmuch as
the latter is a subset of the former, the aim here is to present an elastodynamic reciprocal theorem that also includes elastostatics
as a special case when the time variable becomes irrelevant. This is accomplished by introducing a velocity-based reciprocal
theorem, whose basic properties are subsequently explored. The next step is to use this theorem and formulate a numerical
approach based on boundary integral equation statements and compare them with existing formulations based on conventional
reciprocity relations. The applications presented here involve the standard mechanical oscillator and the unidimensional axial
element as two simple, yet important problems of structural dynamics. Along with the numerical results, a thorough stability
analysis of the corresponding time-stepping algorithms is formulated. In both cases, the superior performance of the methodologies
built on velocity-based reciprocal theorems is clearly demonstrated. 相似文献