无域积分的弹塑性边界元法的非线性互补方法

该文引入非线性互补方法来求解边界元法的弹塑性问题,其中方程组由内部点应力方程和反映塑性本构定律的互补函数形成。涉及的域积分采用径向积分法转化为边界积分。通过受内压的厚壁圆筒的应力、位移和荷载-位移情况表明了该算法的精度。     

边界元法在环境声学中的应用

边界元法是边界积分方程的数值解法 ,是随着计算机技术的发展而出现的。建立声学边界积分方程分两种方法 :直接法与间接法。本文介绍了边界元法在环境声学中的应用 ,如声屏障和不同情况下道路周围的声场分布、复杂气象条件对声传播的影响的问题等。由于边界元法是半解析半数值解法。在解边界积分方程时会遇到解的存在与唯一性问题。     

瞬态弹性动力学问题的半解析边界元法

本文用半解析有限元法对边界积分方程作离散化处理,通过引入基本解函数和半解析半离散试函数的二次半解析过程,使三维弹性动力学问题简化为一维数值计算。文中又采用移动边界元法来模拟波在半无限介质中传播的表面积分问题,分析计算了各种瞬态波在介质内传播,绕射及地面运动问题。计算结果表明,半解析边界元法不仅计算精度高,而且工作量大大降低,具有较高的经济效益与应用价值。     

随机边界元法在大坝可靠性分析中的应用

本文综合考虑重力坝受自重，水压力及温度场的影响，应用随机边界元法，结合一阶二次矩法，分析了一大坝的强度可靠度的稳定可靠度，所得结果与随机有限元法所得相符。     

边界元法分析径向游隙对四列圆锥轴承载荷的影响

 In order to analyze the influence of the radial clearance to the reliability of the four row conical roller bearing, the special calculator program of bearing BEM was compiled based on the method of three dimensional elastic contact boundary element method with frication, in which the plate units were used to simulate the rollers. When equal radial clearance and unequal clearance were applied to the mill four row conical roller bearing, the distribution of radial pressure, radial and axial load were simulated with the program. The influence rules of radial clearance to the pressure and load distribution of four row conical roller bearing were analyzed. According to the result, the load proportion of the mill four row conical roller bearing didnt change when equal radial clearance was adopted. And the number of the standunderload rollers decreased and the load of one roller bearing increased when positive equal radial clearance was adopted. The situation was opposite when negative equal radial clearance was adopted. When unequal radial clearance was adopted, the load proportion of the row with the larger value of radial clearance decreased and the bias factor was decreased．     

边界元法在膜结构与风耦合研究中的应用

膜结构是一种风敏感性结构,结构与风的耦合作用不容忽视。本文将膜结构所处的风场简化为不可压缩势流,运用边界元法求解绕流后作用在膜结构上的风压,然后计算在风压作用下膜结构产生的变形,修正膜结构形状,再次求解变形后膜结构周围流场及作用在其上的风压,这样依次迭代,直至得到收敛的解。这种方法的有效性通过典型算例和其他方法计算结果的对比得到验证。变换膜结构的矢跨比、初始预张力及风场平均风速,研究参数变化对流固耦合的影响,为膜结构抗风研究与工程实践提供参考。     

各向异性外问题的非均匀网格的自然边界元法及其耦合法

本文对于无界区域上各向异性外问题提出了在椭圆边界非均匀网格上的自然边界元法及其与有限元法的耦合法,证明相应的收敛定理和误差估计式,并且在这两种方法中引入基于等分布原理的移动网格技巧.最后,通过数值结果表明了误差收敛理论的正确性以及所提方法和技巧的有效性.     

快速多极子边界元法在吸声材料声场计算中的应用

对快速多极子边界元法中多极子展开式的数值计算进行了研究,建立四点单级传递关系与多极传递关系模型。通过与格林函数及其法向导数理论值的比较,考察两种传递情况下,多极子展开式在吸声材料介质及空气介质中的计算精度。结果表明,复波数展开式的求解精度与截断项数的大小相关,而且当复波数虚部值与展开点间距离乘积过大时,展开式值开始与真值相背离。最后提出了解决此问题的两种方法。此外,以膨胀腔阻性消声器传递损失计算为例,验证了本文方法的有效性与可行性。     

时域径向基函数网络诊断方法在往复泵故障诊断中的应用

往复机械是工程中广泛应用的一种机械设备 ,由于其动力学和运动学形态比旋转机械复杂 ,对其进行故障诊断存在较大难度 ,有效提取往复机械运动中非平稳时变信号中的故障特征和将故障特征准确分类是解决往复机械故障诊断问题的两个关键。本文利用时域数字特征分析方法完成故障特征信息提取 ;通过径向基神经网络对特征信息分类识别 ,实现故障的自动诊断。利用以上原理建立的油田往复塞泵故障监测与诊断系统 ,通过在大庆油田的实际应用表明 ,系统能够比较准确的识别往复柱塞泵多种常见故障 ,且具有较高的运算速度。     

快速多极边界元法在大规模传热分析中的应用

该文将快速多极边界元法用于三维稳态传热问题的大规模数值计算。多极展开的引入使得该算法能够在单台个人电脑上完成30万自由度以上的传热边界元分析。统一展开的基本解能够处理混合边界。广义极小残差法作为快速多极边界元法的迭代求解器,数值算例分析了快速多极边界元法的计算效率。结果表明:快速多极边界元法的求解效率与常规算法相比有数量级的提高;在模拟复杂结构大规模传热问题上将具有良好的应用前景。     

SOLVING NONLINEAR DIFFERENTIAL EQUATIONS OF MECHANICS WITH THE BOUNDARY ELEMENT METHOD AND RADIAL BASIS FUNCTIONS

The Boundary Element Method is a very effective method for solving linear differential equations. To use it also in the consideration of non-linear problems some different procedures were developed, among them the dual reciprocity method and the particular integral method. Both procedures use interpolation conditions for the approximation with radial basis functions. In this paper a method is presented which avoids problems connected with interpolation by means of quasi-interpolation. It is possible to solve differential equations of the kind Δ^mu=p(u) approximately; the application to two non-linear problems of plate theory yield good results. Hints to a theoretical examination of the method including sufficient conditions for feasibility and convergence are given. © 1997 by John Wiley & Sons, Ltd.     

时域内有限元离散方法的探讨

本文提出一种在时域内进行有限元离散的方法。以振动方程为例,详细阐述了这种方法的基本思想,并对计算过程的稳定性进行了讨论,给出一种新的积分格式和若干数值算例。     

自适应有限元线法在二维无穷域问题中的应用

无穷域问题广泛存在于实际工程中,半解析、半离散的数值计算方法—有限元线法（Finite ElementMethod of Lines,简称FEMOL）对其具有较好的适应性。在已有的映射型FEMOL无穷单元理论的基础上,基于单元能量投影（Element Energy Projection,简称EEP）法的自适应FEMOL被应用于二维无穷域问题的求解。用户只需输入稀疏的初始网格和误差限,算法即自动生成优化的FEMOL网格,该网格上常规单元和无穷单元的FEMOL解均按最大模度量满足给定误差限。文中首先介绍二维FEMOL的原理策略、无穷单元的构建,然后概述基于EEP法的自适应FEMOL算法,并讨论其对无穷域问题的适用性,之后对圆柱绕流的Poisson方程问题、带孔无穷大板单向拉伸的弹性力学平面问题、受圆形均布荷载半空间体的三维轴对称问题进行了自适应分析,最终不仅给出了满足误差限的函数（位移）解,也给出了具有优良性态的导数（应力）解,从而为无穷域问题的求解提供了一种高效可靠的新途径。     

CONTINUITY AND COLLOCATION EFFECTS IN THE BOUNDARY ELEMENT METHOD

The presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded. Quite often the continuity conditions, particularly on the derivatives of the density functions, are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions. In this paper, a numerical study on the effects of satisfying or violating the continuity requirements and the effect of the boundary condition collocating point on three different BEM formulations is presented. Two are indirect formulations using force singularities and displacement discontinuity singularities, and the third is Rizzo's direct formulation. The two integral operators in the direct BEM appear individually in the two different formulations of the indirect BEM. This makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct BEM. The impact of the study on numerical modelling for the three BEM formulations is presented in the paper. © 1997 by John Wiley & Sons, Ltd.     

IMPLEMENTATION OF THE BOUNDARY ELEMENT METHOD IN THE DYNAMICS OF FLEXIBLE BODIES

This paper presents the implementation of the Boundary Element Method in the dynamics of flexible multibody systems. Kane's equations are used to formulate the governing boundary initial value problem for an arbitrary three-dimensional elastic body subjected to large overall base motion. Using continuum mechanics principles, direct boundary element incremental formulations are derived. The Galerkin approach was employed to generate the weighted residual statement which serves as a transitory point between continuum mechanics and boundary integral equations. By adapting the updated Langrangian formulation for large displacements analysis and using the Maxwell–Betti reciprocal theorem, integral representations for geometric stiffening were also derived. The non-linear terms were found to be functions of the time-variant stresses associated with the inertial forces at the reference configuration. The domain integrals arising from body forces (such as gravitational loads, inertia loads and thermal loads, etc.) are presented as DRM integrals (Dual-Reciprocity Method). Using the substructuring technique the elastic body is divided into several regions leading to a system of equations whose matrices are sparse (block-banded). The linearized equations of motion were discretized along the boundary of the body, and an algorithm for the integration involving the Houbolt method was used to establish an algebraic system of pseudo-static equilibrium equations. A Newton–Raphson-type iteration scheme was used to solve these discretized balance equations. To take advantage of the sparsity of the matrices, special routines were used to decompose and solve the resulting linear system of equations. An illustrative example is presented to demonstrate the validity of the method as well as how the effects of geometric stiffening effects are captured. The example consists of spin-up manoeuvre of a tapered beam attached to a moving base. The beam was modelled as two-dimensional plane strain problem divided into a number of substructures. Numerical simulation results show how the phenomenon of dynamic stiffening is captured by the present approach.     

全特解场边界元方法在声辐射逆问题中的应用研究

采用全特解场边界元方法求解声辐射逆问题,这种方法不需要变量插值、积分求解及奇性处理,因而计算量大幅度减少,且计算精度高。本文还从辐射声场的情况来探知声源的振动特性,这对噪声的主动控制及低噪声结构优化设计有着很大的意义,为噪声诊断提供直接的依据。     

复合材料边界元素法研究

边界元法是一种迅速发展的数值解法.本文研究了在复合材料层合板中运用平面二次边界元法的有关问题.首先,讨论了将层合板等效为一般正交各向异性单层板的方法;其次,给出了偏轴情况下的基本解,研究了直线型二次边界元偏轴影响系数的解析计算以及域内应力表达式;最后对算例进行了计算,所得结果与相应的解析解和有限元相符甚好.     

弹性地基板广义边值问题的边界元法

本文利用Ｈａｎｋｅｌ变换导出了弹性地基板弯曲问题的基本解，该基本解对于Ｗｉｎｋｌｅｒ地基、Ｐａｓｔｅｒｎａｋ地基和弹性半空间地基模型具有统一的表达形式。在此基础上，建立了适用于弹性地基板广义边值问题的边界积分方程组，最后文中给出了若干数值算例。