基于H - Matrices的结构特征值问题加速研究

提出遗传双重互易法,利用遗传矩阵结构（Hierarchical Matrices , H - Matrices）加速双重互易边界元法（DRBEM）结构特征值问题分析过程并压缩数据存储。通过自适应交叉拟合算法对遗传矩阵中的相容子块使用低阶秩块拟合,减少参与矩阵运算数据规模,降低计算消耗的内存空间。针对规模和效率的不同计算环境要求提出两种求解优化策略,即完全遗传双重互易法(PHDM)和混合遗传双重互易法(MHDM),以求针对性提高数值计算效果。数值算例验证了所提方法的效率以及数据压缩效果。     

Two-dimensional linear elasticity by the boundary node method

This paper presents a further development of the Boundary Node Method (BNM) for 2-D linear elasticity. In this work, the Boundary Integral Equations (BIE) for linear elasticity have been coupled with Moving Least Square (MLS) interpolants; this procedure exploits the mesh-less attributes of the MLS and the dimensionality advantages of the BIE. As a result, the BNM requires only a nodal data structure on the bounding surface of a body. A cell structure is employed only on the boundary in order to carry out numerical integration. In addition, the MLS interpolants have been suitably truncated at corners in order to avoid some of the oscillations observed while solving potential problems by the BNM (Mukherjee and Mukherjee, 1997a) . Numerical results presented in this paper, including those for the solution of the Lamé and Kirsch problems, show good agreement with analytical solutions.     

Analysis of 2-D thin structures by the meshless regular hybrid boundary node method

Thin structures are generally solved by the Finite Element Method (FEM), using plate or shell finite elements which have many limitations in applications, such as numerical locking, edge effects, length scaling and the envergence problem. Recently, by proposing a new approach to treating the nearly-singular integrals, Liu et al. developed a BEM to successfully solve thin structures with the thickness-to-length ratios in the micro- or nano-scales. On the other hand, the meshless Regular Hybrid Boundary Node Method (RHBNM), which is proposed by the current authors and based on a modified functional and the Moving Least-Square (MLS) approximation, has very promising applications for engineering problems owing to its meshless nature and dimension-reduction advantage, and not involving any singular or nearly-singular integrals. Test examples show that the RHBNM can also be applied readily to thin structures with high accuracy without any modification.     

改进的平均源边界节点法模拟平面位势问题

平均源边界节点法ASBNM是一种最近提出的边界型无网格法。该方法仅使用边界节点不涉及任何单元和积分的概念,具有方法简单和程序设计容易等特点。但是,对于依赖于边界积分方程的边界型无网格法,关键问题是如何准确高效地估计影响矩阵的对角元。本文提出直接计算影响矩阵对角元的方法,是已有ASBNM法的改进,将对角元的计算转化为一个纯几何问题,因此适用于任何二维边值问题。数值算例证明了本文方法的有效性和准确性。     

Extension de la DRBEM à la propagation guidée en écoulement cisaillé

The present study aims to extend the Dual Reciprocity Boundary Element Method in order to solve acoustic wave propagation equations in the frequency domain for a parallel shear flow. The Linearized Euler Equations are written as a coupled pair of equations, which are second-order in terms of acoustic pressure and first-order in terms of normal acoustic velocity. Good agreement between numerical results and analytical solutions for a low Mach number shear flow (M<0.1) shows the interest of the method.     

The numerical method for analysing the transient temperature field and transient phase transformation of metal materials in heat treating

In this paper,the Kirchhoffs transformation is popularized to the nonlinear heat conduction problem which the heat conductivity can be expressd as a multinomial of temperature firstly,the boundary condition of heat conduction problem is determined by analytics.Secondly,the incubation peroid superposition and the linear combination law is employed to simulate the transient phasses transformation in the process of heat treatment of materials.That the begin time of phase transformation,the type of phase transformation and the amount of phase constitution is determined simply.Finally,the three-dimension Dual Reciprocity Boundary Element Method is usedto analysis the total process of various heat treatment of component,the results of numerical calculation of examples show that the method provided in this paper is effectivce.     

A structural shape optimization system using the two-dimensional boundary contour method

Summary The research recently conducted has demonstrated that the Boundary Contour Method (BCM) is very competitive with the Boundary Element Method (BEM) in linear elasticity Design Sensitivity Analysis (DSA). Design Sensitivity Coefficients (DSCs), required by numerical optimization methods, can be efficiently and accurately obtained by two different approaches using the two-dimensional (2-D) BCM as presented in Refs. [1] and [2]. These approaches originate from the Boundary Integral Equation (BIE). As discussed in [2], the DSCs given by both BIE-based DSA approaches are identical, and thus the users can choose either of them in their applications. In order to show the advantages of this class of DSA in structural shape optimization, an efficient system is developed in which the BCM as well as a BIE-based DSA approach are coupled with a mathematical programming algorithm to solve optimal shape design problems. Numerical examples are presented. Received 20 July 1998; accepted for publication 7 December 1998     

MESHLESS METHOD OF DUAL RECIPROCITY HYBRID RADIAL BOUNDARY NODE METHOD FOR ELASTICITY

Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.     

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提出了将杂交边界点法和双重互易法结合求解势问题的一种新的算法. 将势问题的解分为通解和特解两部分，通解使用 杂交边界点方法求解，特解则利用局部径向基函数近似. 该方法输入数据只是求解域上离散 的点，不需要额外的方程来计算域内物理量，后处理十分简便. 数值算例表明了该方法的稳 定性和有效性.     

弹性薄板弯曲问题的双互易杂交边界点法

基于一种板的修正变分泛函,将杂交边界点法与双互易法结合,用于薄板弯曲问题的分析。该方法将问题的解分为齐次方程的通解和非齐次的特解两部分,特解采用径向基函数插值得到,而通解则使用杂交边界点法求解。在杂交边界点法用于求解通解的列式过程中,边界变量采用移动最小二乘近似,域内变量则采用基本解插值。与有限元法相比,该方法仅需要边界上离散点的信息,无论插值还是积分都不需要网格,域内点仅用来插值非齐次项,因而仍是一种纯边界类型的无网格方法。数值算例表明,本文方法能以很少的计算自由度获得与其它方法同样的计算精度,且具有前后处理简单、收敛速度快等优点,适合于求解工程中各种薄板的弯曲问题。     

弹性力学平面问题的等价边界积分方程的边界轮廓法

基于边界积分方程中被积函数散度为零的特性,提出了弹性力学平面问题的等价边界积分方程的边界轮廓法,该方法无需进行数值积分,只需要计算单元两结点势函数值之差。实例计算说明,基于传统的边界积分方程的边界轮廓法所得到的面力结果是错误,而本文建立的边界轮廓法则可给出精确的结果。     

三维弹性快速多极边界元法

将静电场多极展开法和广义极小残值法结合于三维弹性问题的边界元法，使其求解的计算量及所需内存量同节点的自由度总数成正比，变革计算结构，加快求解速度以适应大规模数值计算。两者结合的关键点在于边界元法基本解的合理分解，并用广义极小残值法(GMRES)求解方程。轧机支承辊变形场大规模数值算例的总自由度数首次达N=34008并获得成功。清晰地描述了支承辊和工作辊接触区的辊型。     

弹性动力学的双互易杂交边界点法

将双互易法同杂交边界点法相结合,提出了求解弹性动力问题的新型数值方法------双互易杂交边界点方法. 该算法在求解弹性动力问题时,将控制方程非齐次项的域内积分转化为边界积分. 该方法将问题的解分为通解和特解两部分,通解使用杂交边界点法求得,特解则使用局部径向基函数插值得到,从而实现了使用静力问题的基本解来求解动力问题. 计算时仅仅需要边界上离散点的信息,无论积分还是插值都不需要网格,域内节点仅用来插值非齐次项,因此该算法仍是一种边界类型的无网格方法. 数值算例表明,该方法后处理简单,计算精度高,适合于求解弹性动力问题.      

MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD

The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.     

CONSERVATION LAWS IN FINITE MICROCRACKING BRITTLE SOLIDS

This paper addresses the conservation laws in finite brittle solids with microcracks. The discussion is limited to the 2-D cases. First, after considering the combination of the Pseudo-Traction Method and the indirect Boundary Element Method, a versatile method for solving multi-crack interacting problems in finite plane solids is proposed, by which the fracture parameters （SIF and path-independent integrals） can be calculated with a desirable accuracy. Second, with the aid of the method proposed, the roles the conservation laws play in the fracture analysis for finite microcracking solids are studied. It is concluded that the conservation laws do play important roles in not only the fracture analysis but also the analysis of damage and stability for the finite microcracking system. Finally, the physical interpretation of the M-integral is discussed further. An explicit relation between the M-integral and the crack face area, i.e., M = GS, has been discovered using the analytical method, which can shed some light on the Damage Mechanics issues from a different perspective.     

Stochastic boundary element method in elasticity

The stochastic boundary element method is developed to analyze elasticity problems with random material and/or geometrical parameters and randomly perturbed boundaries. Based on the first-order Taylor series expansion, the boundary integration equations concerning the mean and deviation of the displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random body force, so the mean and covariance matrices of unknown boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of displacements and stresses at inner points can also be obtained. Numerical examples show that the proposed stochastic boundary element method gives satisfactory solutions, as compared with those obtained by theoretical analysis or other numerical methods. The project supported by the National Natural Science Foundation of China and the State Education Commission Foundation of China     

不可压粘流N－S方程的边界积分解法

对原变量的Ｎ－Ｓ方程进行一阶时间离散，采用共轭梯度法解除压强－速度的耦合．对所得的一系列Ｌａｐｌａｃｅ方程、Ｐｏｓｓｉｏｎ方程和Ｈｅｌｍｈｏｔｚ方程均进行边界积分法求解，首次得到了粘性Ｎ－Ｓ方程的边界积分表示式．圆柱的定常、非定常尾迹计算结果表明了本文方法的有效性．     

不可压粘流N－S方程的边界积分解法

对原变量的Ｎ－Ｓ方程进行一阶时间离散，采用共轭梯度法解除压强－速度的耦合．对所得的一系列Ｌａｐｌａｃｅ方程、Ｐｏｓｓｉｏｎ方程和Ｈｅｌｍｈｏｔｚ方程均进行边界积分法求解，首次得到了粘性Ｎ－Ｓ方程的边界积分表示式．圆柱的定常、非定常尾迹计算结果表明了本文方法的有效性．     

AN IMPROVED HYBRID BOUNDARY NODE METHOD IN TWO-DIMENSIONAL SOLIDS

The hybrid boundary node method （HBNM） is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares（MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the latter. Following its application in solving potential problems, it is further developed and numerically implemented for 2D solids in this paper. The rigid movement method is employed to solve the hyper-singular integrations. Numerical examples for some 2D solids have been given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method are studied through numerical examples.     

Dynamic point sources in laminated media via the thin-layer method

This paper presents closed-form expressions for the Greens functions associated with harmonic point sources acting within horizontally layered media. These expressions are intended for use with the highly efficient Thin-Layer Method (TLM) described elsewhere, which is now being used widely for diverse engineering purposes. Among the dynamic sources considered are point forces, force dipoles (cracks and moments) , blast loads, seismic double couples with no net resultant, and bimoments (moment dipoles) . Comparisons with known analytical solutionsfor homogenous media demonstrate the accuracy of the formulation. However, the main field ofapplication is laminated media, for which no analytical solutions can be obtained. On the otherhand, it should be noted that the computational effort in this method does not depend on whetherthe system is layered. The resulting Greens functions could be used to efficiently model elasticwaves in complex media by means of the Boundary Integral Method.