THE BEM FOR SOLVING THE NONHOMOGFNEOUS HELMHOLTZ EQUATION WITH VARIABLE COEF

ＷａｎｇＳｈｏｕｘｉｎ（王守信）；ＬｉｕＸｉｐｉｎｇ（刘喜平）；ＰｅｎｇＴｉａｎｇｕｏ（彭天国）；ＺｈａｏＺｈｏｎｇｓｈｅｎｇ（赵忠生）；ＺｈａｏＳｕｈｕａ（赵素华）（ＲｅｃｅｉｖｅｄＮｏｖ．１１．１９９４；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＬｉｎＺｏｎｇ...     

A HIGH ORDER KERNEL INDEPENDENT FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR ELASTODYNAMICS

基于核无关的快速多极方法, 发展了一种弹性动力学问题的快速、高精度边界元分析方法. 采用基于二次曲面单元的Nyström 离散, 将边界积分方程转化为求和形式, 可以方便地进行加速计算;由于采用二次元, 边界元分析精度很高. 将一种新型快速多极方法用于Nyström 边界元法的加速计算, 该方法的数值实现简便、不依赖于积分方程基本解的表达式, 因此通用性很好;该方法还具有最优的计算量和存储量、精度高且可以控制. 结合Nyström 边界元系数矩阵和快速多极方法转换矩阵的特点, 提出一种大幅度降低边界元内存消耗的策略. 数值结果表明, 该方法无论在分析精度, 还是计算速度和内存消耗上, 都大大优于同类方法, 是一种快速、通用的工程弹性动力学问题大规模数值分析方法.     

Boundary element method for model analysis of 2-D composite structure

The boundary element method is used for the modal analysis of free vibration of 2-D composite structures in this paper. Since the particular solution method is used to treat the terms of body forces (inertial forces) in the equation of motion, only static fundamental solutions are needed in solving the problem. For an isotropic cantilever beam, the numerical results obtained by using the BEM presented in this paper are in good agreement, with, those of using FEM or other BEM, but this BEM can also be used to analyze problems for anisotropic materials. For simply supported composite laminated beams, the comparisons of the numerical reslts obtained by this method with the analytical results obtained by 1-D laminated beam theory indicate that if the ratio of length/thickness is greater than 20, the results of the two methods are in good agreement, but if the ratio of length/thickness is less than 20, big errors will occur for 1-D laminated beam theory.     

确定疲劳极限的外推法

提出了利用成组法的结果代替升降法确定疲劳极限的外推法。首先给出以疲劳极限为参量的S－N曲线的数学表达式。然后将四组成组法的试验结果代入上式，得到四个等式。从这四个等式中消去其它的材质参量，即可得到求解疲劳极限的超越方程。在求得疲劳极限后，再根据上述试验结果以最小二乘法拟合上述其它材质参量。利用该方法可进一步做出完整的中值S－N曲线，这就大大地节约了疲劳试验的机时与疲劳试验费用。     

二维复合材料结构模态分析的边界元法

将边界元方法用于分析二维复合材料结构的自由振动模态，利用特解处理体积力（惯性力）仅需静态基本解就可求解问题，对一各向同性悬臂梁，用该法得到的结果与用有限元或各向性边界元法得到的结果符合得很好，但该法可解各向异性问题，对层状复合材料简支梁，用该法得到了数值结果与用一维层状复合材料梁的理论解的比较表明，当结构的长厚比大于２０时，二者符合得很好，当结构的长厚比小于２０时，一维层状材料梁的理论将产生很大的     

Solution of the Navier–Stokes equations in velocity–vorticity form using a Eulerian–Lagrangian boundary element method

This paper describes the Eulerian–Lagrangian boundary element model for the solution of incompressible viscous flow problems using velocity–vorticity variables. A Eulerian–Lagrangian boundary element method (ELBEM) is proposed by the combination of the Eulerian–Lagrangian method and the boundary element method (BEM). ELBEM overcomes the limitation of the traditional BEM, which is incapable of dealing with the arbitrary velocity field in advection‐dominated flow problems. The present ELBEM model involves the solution of the vorticity transport equation for vorticity whose solenoidal vorticity components are obtained iteratively by solving velocity Poisson equations involving the velocity and vorticity components. The velocity Poisson equations are solved using a boundary integral scheme and the vorticity transport equation is solved using the ELBEM. Here the results of two‐dimensional Navier–Stokes problems with low–medium Reynolds numbers in a typical cavity flow are presented and compared with a series solution and other numerical models. The ELBEM model has been found to be feasible and satisfactory. Copyright © 2000 John Wiley & Sons, Ltd.     

基于预估-校正的Generalized-α法及其在非线性结构动力学中的应用

直接积分法是求解动力学方程的一种有效方法。应用一种预估-校正的Generalized-α法对结构大变形动力学问题进行分析求解,并与Newmark法和Bathe法进行对比研究。首先预估当前计算步的解,然后以预估值作为起始值进行非线性迭代计算,并对解不断校正,直到满足收敛条件,进入下一时间步的计算。在保证Generalized-α法性能的基础上,简化了非线性迭代公式,便于编程实现。通过壳和实体的大变形动力学算例,证明了本文方法具有较高的稳定性和精度。     

弹性动力学高阶核无关快速多极边界元法

基于核无关的快速多极方法, 发展了一种弹性动力学问题的快速、高精度边界元分析方法. 采用基于二次曲面单元的Nystr?m 离散, 将边界积分方程转化为求和形式, 可以方便地进行加速计算;由于采用二次元, 边界元分析精度很高. 将一种新型快速多极方法用于Nystr?m 边界元法的加速计算, 该方法的数值实现简便、不依赖于积分方程基本解的表达式, 因此通用性很好;该方法还具有最优的计算量和存储量、精度高且可以控制. 结合Nystr?m 边界元系数矩阵和快速多极方法转换矩阵的特点, 提出一种大幅度降低边界元内存消耗的策略. 数值结果表明, 该方法无论在分析精度, 还是计算速度和内存消耗上, 都大大优于同类方法, 是一种快速、通用的工程弹性动力学问题大规模数值分析方法.      

用子域边界元法研究各向异性材料中的界面裂纹

用子域边界元法研究各向异性材料中的界面裂纹，在边界元公式中，采用了带特征根的基本解，以增量形式的边界积分方程为基础，通过二次等参元及国分之一面力奇异远离散化处理，可以得到各子域的代数方程组，依据凝集技术，可得到仅含有子域公共边界及裂纹边界未知量的求解方程组，通过迭代法，可以寻求到每种载荷作用下的裂纹所处的真实状态，然后，由文献「２」中的方法求解界面裂纹的应力强度因子。结果表明，子域边界方法是正确的     

Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory

Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube (SWCNT) subjected to a harmonic load is investigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.     

基于行消元回代法的多域边界元分析方法

提出了一种用多域边界元技术求解大型工程问题的新算法. 首先, 采用三步变量凝聚技术, 将由内部点、边界点和公共结点表述的每一子域的基本边界元代数方程表述成只有公共结点变量为未知量的代数方程, 然后, 根据公共结点的平衡方程和协调条件组集具有稀疏系数特征的总体系统方程组. 为了有效求解该系统方程组, 首次在边界元法中引进一种能有效求解大型非对称稀疏系数矩阵方程组的行消元回代法(REBSM), 该方法可在方程的每一行组形成时进行消元和回代, 当方程组组集完毕后即可得到方程的解, 不需要最后的回代过程. 因为一些项的重复计算在每一行的处理中合并掉, 因此REBSM要比传统的高斯消元法需要较少的内存, 而且计算速度具有数量级的提高, 可为边界元法求解大型工程问题提供有力的方程求解器.      

An adaptive numerical scheme for solving incompressible 2‐phase and free‐surface flows

In this paper, we present a numerical scheme for solving 2‐phase or free‐surface flows. Here, the interface/free surface is modeled using the level‐set formulation, and the underlying mesh is adapted at each iteration of the flow solver. This adaptation allows us to obtain a precise approximation for the interface/free‐surface location. In addition, it enables us to solve the time‐discretized fluid equation only in the fluid domain in the case of free‐surface problems. Fluids here are considered incompressible. Therefore, their motion is described by the incompressible Navier‐Stokes equation, which is temporally discretized using the method of characteristics and is solved at each time iteration by a first‐order Lagrange‐Galerkin method. The level‐set function representing the interface/free surface satisfies an advection equation that is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level‐set function (redistancing) as well as the construction of a convenient flow for the level‐set advection equation. Numerical results are presented for both bifluid and free‐surface problems.     

Numerical computation of solitary wave solutions of the Rosenau equation

We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then apply two numerical algorithms based on the Petviashvili method for solving the Rosenau equation with single or double power law nonlinearity. Numerical calculations rely on a uniform discretization of a finite computational domain. Through some numerical experiments we observe that the algorithm converges rapidly and it is robust to very general forms of the initial guess.     

A DOMAIN DECOMPOSITION ALGORITHM WITH FINITE ELEMENT-BOUNDARY ELEMENT COUPLING

A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method (FEM) and the boundary element method (BEM). The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element (FE-BE) coupling method.     

Simulation of unsteady turbulent flows around moving aerofoils using the pseudo‐time method

The pseudo‐time formulation of Jameson has facilitated the use of numerical methods for unsteady flows, these methods have proved successful for steady flows. The formulation uses iterations through pseudo‐time to arrive at the next real time approximation. This iteration can be used in a straightforward manner to remove sequencing errors introduced when solving mean flow equations together with another set of differential equations (e.g. two‐equation turbulence models or structural equations). The current paper discusses the accuracy and efficiency advantages of removing the sequencing error and the effect that building extra equations into the pseudo‐time iteration has on its convergence characteristics. Test cases used are for the turbulent flow around pitching and ramping aerofoils. The performance of an implicit method for solving the pseudo‐steady state problem is also assessed. Copyright © 2000 John Wiley & Sons, Ltd.     

基于PID方法的可倾瓦推力轴承分析

使用PID方法控制可倾瓦推力轴承流场求解中轴瓦倾角和支点膜厚的迭代,实现了力和力矩平衡同步收敛.以光滑及粗糙表面下可倾瓦推力轴承流场求解为例,对比PID方法和传统方法,PID法编程便捷,计算效率高,同时能够反映可倾瓦推理轴承的刚度特性.考虑表面粗糙度时,PID法能够求解传统方法不收敛的问题.     

三维声学特征频率灵敏度分析的边界元法

声系统特征频率的灵敏度分析为其优化设计提供了基础,具有重要意义。边界元法在声学问题的求解中具有独特优势,但因其系统方程系数矩阵的频率相关性导致的非线性特征值问题给声学特征频率的灵敏度分析带来了很大困难。为此,本文首先对非线性特征值问题进行了线性化处理,利用围道积分投影方法将非线性特征方程转换为小规模广义特征方程,然后对其关于设计变量直接求导,并引入左特征向量和转换矩阵构造了一种适用于内外声场的三维声学单/重特征频率灵敏度分析的边界元法。数值算例验证了该方法的适用性,以及对单/重特征频率灵敏度的计算精度。     

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.     

三维热权函数法和多虚拟裂纹扩展技术

热权函数法直接利用温度场与热权函数的乘积的积分来求应力强度因子(SIF)的过渡过程，它可以免除对每一时刻进行热弹性力学有限元或边界元应力分析，计算效率大大提高。本文给出了三维热权函数法的基本方程，并提出了求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE法)。在MVCE法中，可以引入无穷多个虚拟裂纹扩展模式；虚拟裂纹扩展模式与应力强度因子的插值直接相联系，所得到的方程组的系数矩阵是一个三对角矩阵，具有良好的计算性能。它对于裂纹前缘SIF分布急剧变化的情况，有良好的数值模拟能力。实例计算表明，MVCE法具有权高的计算效率，并具有很高的计算精度。     

埋入水中旋转薄壳谐耦振分析的传递矩阵法

基于一般线弹性薄壳和势流理论,导出了旋转壳状态向量的一阶常微分矩阵方程和水动压力表达式,再借助齐次扩容技术和精细积分法,应用推广的传递矩阵法对埋入水中旋转薄壳的流固耦振进行了数值求解,并研究了一些因素对精度的影响.算例表明传递矩阵法和有限元方法相比不仅精度良好,而且有较高的计算效率.