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。     

Application of dual kriging to structural shape optimization based on the boundary contour method

Summary The paper presents an approach in which the coupling of dual kriging and the boundary contour method (BCM) is applied to structural shape optimization problems in mechanical engineering design. The problems consist of optimizing the shape of an elastic body, which requires minimizing an objective function subject to some given constraints, such as those of displacement, stress or manufacturing. The originality of the present work is involved with the use of two novel methods that are combined here to solve structural shape optimization problems. The first one, called dual kriging, is a general, versatile interpolation and geometric modeling tool. The second one is a new variant of the boundary element method (BEM), called the BCM, which achieves a further reduction in dimensionality of analysis problems. Based on the advantages of these two methods, the coupling approach presented here is expected to offer an effective as well as a straightforward manner for solving shape optimal design problems. Received 18 December 1997; accepted for publication 21 April 1998     

平面问题等价边界积分方程的三次边界轮廓法

基于弹性力学平面问题等的边界积分方程,给出了三次单元的边界轮廓法。根据平面问题解的复变函数表示,构造了三次形函数。给出了对于混合边值问题求解系统方程确定的边界轮廓方程配置和三次单元界轮廓法的实施。     

形状设计灵敏度分析的改进的再生核质点法

基于物质导数概念和直接微分法,将再生核质点法应用于形状设计灵敏度分析（DSA）中。导出了基于无网格近似的灵敏度方程,特别强调了在考虑形状函数关于设计变量的物质导数时无网格方法与有限元法的不同。通过对RKPM形状函数及其物质导数进行矩式显式表述,提高了无网格方法的计算效率。对两个二维线弹性问题进行了位移灵敏度和应力灵敏度分析,计算结果与解析解吻合的很好;同时通过对通常的RKPM和改进的RKPM计算耗时的比较,显示了该方法不仅有效,而且可以显著地提高计算效率。     

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR THREE-DIMENSIONAL ELASTICITY WITH BODY FORCE

Combining Dual Reciprocity Method （DRM） with Hybrid Boundary Node Method （HBNM）, the Dual Reciprocity Hybrid Boundary Node Method （DRHBNM） is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.     

2‐D transmitral flows simulation by means of the immersed boundary method on unstructured grids

Interaction between computational fluid dynamics and clinical researches recently allowed a deeper understanding of the physiology of complex phenomena involving cardio‐vascular mechanisms. The aim of this paper is to develop a simplified numerical model based on the Immersed Boundary Method and to perform numerical simulations in order to study the cardiac diastolic phase during which the left ventricle is filled with blood flowing from the atrium throughout the mitral valve. As one of the diagnostic problems to be faced by clinicians is the lack of a univocal definition of the diastolic performance from the velocity measurements obtained by Eco–Doppler techniques, numerical simulations are supposed to provide an insight both into the physics of the diastole and into the interpretation of experimental data. An innovative application of the Immersed Boundary Method on unstructured grids is presented, fulfilling accuracy requirements related to the development of a thin boundary layer along the moving immersed boundary. It appears that this coupling between unstructured meshes and the Immersed Boundary Method is a promising technique when a wide range of spatial scales is involved together with a moving boundary. Numerical simulations are performed in a range of physiological parameters and a qualitative comparison with experimental data is presented, in order to demonstrate that, despite the simplified model, the main physiological characteristics of the diastole are well represented. Copyright © 2002 John Wiley & Sons, Ltd.     

On accurate boundary conditions for a shape sensitivity equation method

This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier–Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least‐squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite‐element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd.     

Electro-mechanical coupling analysis of MEMS structures by boundary element method

In this paper, we present the applications of Boundary Element Method (BEM) to simulate the electro-mechanical coupling responses of Micro-Electro-Mechanical systems (MEMS). The algorithm is programmed in our research group based on BEM modeling for electrostatics and elastostatics. Good agreement is shown while the simulation results of the pull-in voltages are compared with the theoretical/experimental ones for some examples. The project supported by the 973 Program (G199033108) and the national Natural Science Foundation of China (10125211)     

移动最小二乘浸没边界法中的权函数影响分析

考察了浸没边界法中运用移动最小二乘法构造的插值形函数的影响。通过在移动最小二乘法中采用不同的权函数,分析了相应的插值形函数的性质,并与传统的离散delta函数做了比较。以静止流体中的水平振荡圆柱为例,阐明了形函数对圆柱阻力系数的幅值和光滑性的影响,得到了较优的形函数分布,并将结果与文献对比验证了本文方法的可靠性。     

等深度螺旋槽止推轴承的边界元法计算

本文以分析等深度螺旋槽止推轴承为例,介绍了边界元法在润滑力学研究领域中的应用。以及相应的边界条件的处理方法,并且讨论了轴承尺寸参数对性能参数的影响。     

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.     

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.     

A boundary element method for calculating elastic waves scattered by axisymmetric inclusion

A Boundary Element Method (BEM) is described to compute the scattering of elastic waves by an axisymmetric inclusion in an infinite elastic medium. The boundary loads applied to the inclusion is expanded in terms of Fourier series in an infinite space. The boundary integral equation is solved in the general direction of the axisymmetric inclusion by BEM. The problem of the 3-D scattering of elastic waves is reduced to a 1-Done. According to the geometric features of the axisymmetric in clusion the ring shell elements are adopted in this method. A comparison is made with other BEM methods. The numerical results show this method can reduce the amount of calculation and enhance the speed of convergence. Supported by Foundation of Ph. D Program of State Education Commission of China     

Application of BEM and optimization technique to wear problems

In this paper a new method for solving wear problems, using the Boundary Element Method (BEM) is proposed. The proposed method uses a shape optimization technique for rapid calculation of the maximum wear depth and the final geometry of the bodies in contact after a specified service period. The optimization method solves the wear problem directly, without using increments of the sliding distance as in the classical methods. The BEM is used for modelling both bodies in contact, treating the problem as a multi-region problem. The material loss is presented in terms of the applied load and the sliding distance, and is modelled using a linear wear model. The proposed method is shown to be robust as it requires only few iterations to achieve a converged solution. The reduction in computational effort, as compared to the classical incremental method, becomes more significant as the sliding distance increases.     

自由面势流问题边界元法的数值色散误差

以连续及离散Fourier分析研究自由面势流问题边界元法的数值色散误差,并从理论上探讨有关计算中数值色散误差的改善问题.研究表明:对于该问题的数值色散误差而言,重要的在于以问题相应的离散算子考察计及各种数值手段后的总体色散误差,而非仅考虑该数值手段自身的数值色散误差大小.高阶面元、自由面域外奇点或适当的耦合方法是降低有关问题算子总体色散误差的较好选择.     

The boundary contour method for magneto-electro-elastic media with quadratic boundary elements

This paper presents a development of the boundary contour method (BCM) for magneto-electro-elastic media. First, the divergence-free of the integrand of the magneto-electro-elastic boundary element is proved. Second, the boundary contour method formulations are obtained by introducing quadratic shape functions and Green’s functions [Ding, H.J., Jiang, A.M., 2004. A boundary integral formulation and solution for 2D problems in magneto-electro-elastic media. Computers and Structures, 82 (20–21), 1599–1607] for magneto-electro-elastic media and using the rigid body motion solution to regularize the BCM and avoid computation of the corner tensor. The BCM is applied to the problem of magneto-electro-elastic media. Finally, numerical solutions for illustrative examples are compared with exact ones. The numerical results of the BCM coincide very well with the exact solution, and the feasibility and efficiency of the method are verified.     

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．     

基于整体-局部技术的结构形状优化策略

针对大尺度结构局部形状优化设计中的求解效率与精度之间的矛盾,提出了一种基于整体-局部技术的结构形状优化方法.首先,分析并讨论了是否考虑对切割边界的边界条件进行修正的两种优化方案的优缺点.然后,提出了一种将整体-局部技术与无梯度优化法相结合的双循环优化程序.最后,通过一系列实例对双循环优化程序的实用性、效率和结果精度进行了验证分析.结果 表明,提出的基于整体-局部技术的结构形状优化策略对解决大尺度结构局部形状优化问题,无论是在计算效率还是在结果精度方面,都具有很好的效果.     

A numerical implementation using mid-node collocation for the hypersingular boundary contour method

A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional problems does not require any numerical integration at all. In another development, a boundary contour implementation of a regularized hypersingular boundary integral equation (HBIE) using quadratic elements and end-node collocation was proposed and the technique is termed the hypersingular boundary contour method (HBCM). As reported in that work, the approach requires highly refined meshes in order to numerically enforce the stress continuity across boundary contour elements. This continuity requirement is very crucial since the regularized HBIE is only valid at collocation points where the stress tensor is continuous, while the computed stress at the endpoints of a boundary contour element, which is a non-conforming element, is generally not. This paper presents a new implementation of the HBCM for which the regularized HBIE is collocated at the mid-node of a boundary contour element. As the computed stress tensor is continuous at these mid-nodes, there is no need for unusually refined meshes. Some numerical tests herein show that, for the same mesh density, the HBCM using mid-node collocation has a comparable accuracy as the BCM.     

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．