Taylor级数多极边界元法及其在轧制工程中的应用

通过基本解的多极展开与边界元线性方程组的隐式求解方法(GMRES)相结合,开发出了快速多极边界元法。Taylor级数多极边界元法更新了传统边界元法的求解模式,大大提高了计算效率,扩大了边界元法的求解规模。介绍了Taylor级数多极边界元法的发展历史和现状,给出了Taylor级数多极边界元法的基本思想、基本原理和分类,给出了基本解的Taylor展开方法和边界积分的基本实现步骤。将该方法应用于轧制工程中,通过轧辊弹性变形和HC轧机辊系接触和变形的数值解析,说明了Taylor级数多极边界元法适合于大规模轧制工程     

Mathematical Programming Solution for the Frictional Contact Muitipole BEM

This paper presents a new mathematical model for the highly nonlinear problem of frictional contact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic contact with friction to replace the Monte Carlo method. A numerical example shows that the optimization programming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conventional BEM.     

Mathematical Programming Solution for the Frictional Contact Multipole BEM

IntroductionElastic friction contact problems require accuratetracking of the movement of objects before and aftercontact and the interaction during contacts and correctsimulation of the frictional behavior between the con-tact surfaces. The boundary element method (BEM)[1,2]is well suited to accurately describe the variation of thefrictional contact conditions since the highly nonlineareffects only occur on the contact surface. For nonlinear frictional contact, various approacheshave been …     

Fast Multipole BEM for 3-D Elastostatic Problems with Applications for Thin Structures

The fast multipole method (FMM) has been used to reduce the computing operations and memory requirements in large numerical analysis problems. In this paper, the FMM based on Taylor expansions is combined with the boundary element method (BEM) for three-dimensional elastostatic problems to solve thin plate and shell structures. The fast multipole boundary element method (FM-BEM)requires O(N) operations and memory for problems with N unknowns. The numerical results indicate that for the analysis of thin structures, the FM-BEM is much more efficient than the conventional BEM and the accuracy achieved is sufficient for engineering applications.     

固体力学中快速多极边界元法研究进展

和快速多极方法相结合，使边界元法处理大规模工程与科学问题变得十分有效,首先概括介绍了快速多极边界元法，接着介绍其精度和效率的验证以及与常规边界元法的比较，并给出在微机机群上的快速多极边界元并行算法,给出了快速多极边界元法的一些应用，其中包括：复合材料的二维、三维模拟，含大量裂纹的二维弹性固体及其疲劳裂纹扩展的模拟．此外还介绍了用于弹塑性问题的快速多极边界元新方法．     

压力容器开孔结构分析的快速多极边界元研究

压力容器开孔结构的应力高度集中。为精确模拟该结构的应力状况,该文提出一种三维高阶快速多极边界元法。在三维弹性力学边界元法的基础上,推导出二阶单元的基本解快速多极展开格式。该算法通过多极展开概念,大大降低了对存储量的要求,并且不损失精度。使用高阶快速多极边界元法分析含多个开孔的压力容器整体结构,所得应力结果与大规模高阶有限元法的结果吻合得很好。研究结果表明,高阶快速多极边界元法易于分析此类大规模问题,并具有很高的数值计算精度,满足工程设计的要求。     

Taylor级数多极边界元法远场影响的误差估计

快速多极方法能够有效地提高边界元法的计算效率．求解的计算量和内存量与问题的自由度数N成正比．求解的精度与传统边界元法相比有所下降．分析了Taylor级数多极边界元法的计算精度和远场影响系数的误差．研究了核函数r的Taylor级数展开性质,推导了三维弹性问题基本解的误差估计公式．说明了影响多极边界元法计算精度的因素．数值算例显示了误差估计公式的正确性和有效性．     

一种新的用于二维弹性静力学的快速多极边界元法

快速多极边界元法(fastmultipole BEM)是近几年发展起来的边界元新型算法。本文提出了一种新型的适合二维弹性静力学问题的快速多极边界元格式，并用于含有多个夹杂的二维复合材料的应力分析。数值结果表明这种方法非常适合解决大规模问题。     

三维快速多极边界元高性能并行计算

该文实现了快速多极边界元法的一种高性能并行计算。其并行求解器基于自适应新版本快速多极边界元算法,采用三维二次等参元和等精度积分格式,并通过实测的任务量进行分布式并行环境下的合理负载划分。数值算例表明,该求解器在保持高次边界元高精度优点的基础上,对于几何形状不规则的结构仍能保持较好的并行效率,和传统边界元法相比使解题规模有了数量级的提高。这种并行计算为边界元法在大规模复杂工程问题中的应用提供了有效方案。     

随机分布圆孔板有效弹性模量快速多极虚边界元法模拟

将快速多极算法和广义极小残值法(GMRES)结合于虚边界元法的方程求解,形成了快速多极虚边界元法的求解思想.本方法采用了"源点"多极展开和"场点"局部展开的组合处理方案,使得原问题方程组求解的计算耗时量和储存量均降至与所求问题的计算自由度数成线性比例.文中分析了含随机分布多圆孔板的有效弹性模量,并与其它数值方法的结果进行了比较,同时数值验证了本方法的可行性、计算精度及计算效率.     

Multipole BEM for 3-D Elasto-Plastic Contact with Friction

The analysis of 3-D elasto-plastic contact with friction is a highly nonlinear problem. The elements in the contact and plastic zones should be refined to obtain accurate information about the real size,displacement, and traction in the contact zone. However, the increase in the number of degrees of freedom is limited when traditional boundary element method (BEM) is used with the larger memory size and long CPU time required for the solution procedure. This paper describes the additional mathematical friction model to the 3-D elastic multipole BEM to develop a 3-D elasto-plastic contact multipole BEM. Numerical tests show that with this new method, the needed computer memory size is only 2% of the traditional BEM model with friction, which erases large-scale computing with refined meshes and improves the computational accuracy.     

大变形条件下纤维增强复合材料的有效性能

纤维增强树脂基复合材料具有优异的力学性能,其应用领域十分广阔．在其中的许多应用中,复合材料会发生大变形．本文建立了大变形条件下纤维增强树脂基复合材料的细观力学模型和均匀化方法,计算了复合材料在不同应变情况下的有效切线模量,研究了纤维性能、体分比和组成方式对复合材料有效性能的影响．研究表明,在大变形条件下,复合材料的有效切线性能随着纤维性能和体分比的提高而显著提高,而纤维束增强复合材料的有效切线性能要优于单丝纤维增强复合材料的有效切线性能．     

SEM in situ laboratory investigations on damage growth in GFRP composite under three-point bending tests

Glass fiber-reinforced polymer (GFRP) composites are widely used in low-weight constructions.SEM (scanning electron microscopy) in situ experiments of damage growth in GFRP composite under three-point bending loads are carried out.By summarizing the experimental results of three groups of samples with different orientation angles of fibers,the dependence of mechanical parameters on the orientation angles of fibers are analyzed.The regression analysis show that the peak strengths,the elastic strengths and th...     

均匀化方法在C／C复合材料中的应用研究

将均匀化理论与有限元法相结合应用于碳／碳复合材料有效弹性性能的求解计算中。通过与实验及文献结果的比较，验证了均匀化有限元方法的有效性；同时，还考察了参数对该材料等效性能的影响，得到了具有一定指导意义的结果。     

FM-BEM Evaluation for Effective Elastic Moduli of Microcracked Solids

A fast multipole boundary element method (FM-BEM) was applied for the analysis of microcracked solids. Both the computational complexity and memory requirement are reduced to O(N), where N is the number of degrees of freedom. The effective elastic moduli of a 2-D solid containing thousands of randomly distributed microcracks were evaluated using the FM-BEM. The results prove that both the differential method and the method proposed by Feng and Yu provide satisfactory estimates to such problems. The effect of a non-uniform distribution of microcracks has been studied using a novel model. The numerical results show that the non-uniform distribution induces a small increase in the global stiffness.     

快速多极边界元法在薄板结构中的应用

基于Taylor级数多极展开研究了边界元快速多极算法(FM—BEM)，并将它应用于薄板结构。算例分析表明FM—BEM的计算时间和存储空间明显少于常规边界元迭代解法。随着问题规模的增大，这种优势将更加突出。     

FMBEM求解直圆柱线性波绕射问题

运用快速多极子边界元法(Fast Multipole Boundary Element Method,FMBEM)求得单圆柱在线性波浪中的绕射问题的数值解.所谓的快速多极子边界元法就是采用快速多极子法(Fast Multipole Method,FMM)加速传统边界元法的求解速度.在文中通过求解二维的Helmholtz方程证明FMBEM法具有高精度和高效率,适用于求解大规模的数值问题.另外,给出了单圆柱线性平面波绕射问题中相关水动力学系数的数值计算结果.     

Micromechanics-BEM Analysis for Piezoelectric Composites

The effective material properties of piezoelectric composites are predicted using micromechanics models of the composite structure combined with a boundary element method (BEM) solution of the governing equation. The composites consist of inclusion and matrix phases. The micromechanics method gives formulae for the overall material constants as functions of the concentration matrix, while the boundary element simulation gives numerical solutions of the boundary displacement and electric potential equations for inclusion or hole problems. Numerical results for a piezoelectric plate with circular inclusions are presented to illustrate applications of the proposed micromechanics-BEM formulation.     

含弱界面的复合材料层合板对水平剪切波的散射

对含有弱界面的复合材料层合板,采用弱连接界面的剪切弹簧模型,借助波函数法研究了水平剪切波入射时层合板对波的散射,得到了解析结果.数值计算结果表明,弱界面处在不同位置时,对以一定角度入射到复合材料层合板的水平剪切波,其反射和透射系数有明显变化;当层合板中弱界面的力学性能参数强弱不同时,以入射角为变量所得到的透射系数和反射系数曲线呈现出明显差异.证明了根据含弱界面复合材料层合板所得到的水平剪切波的散射规律,不仅能够确定反映弱界面力学性质的参数R的大小,而且还能够判明弱界面所在的位置,这将为复合材料层合板中弱界面的超声无损检测提供依据.     

机械弹性车轮侧向刚度的影响因素分析

为深入研究机械弹性车轮侧向力学特性,基于理论及数值仿真的方法对车轮侧向刚度影响因素进行了分析.利用能量法建立了0轮单元侧向刚度理论模型,并得到影响车轮侧向刚度的主要因素.在简化机械弹性车轮结构的基础上,建立了车轮三维有限元模型,并验证了模型的有效性.针对不同垂向载荷、0轮几何结构参数以及橡胶层剪切模量,对机械弹性车轮进行了侧向刚度特性的仿真试验.计算结果表明:随着垂向载荷、橡胶层剪切模量的增大,车轮侧向刚度均增大;随着0轮断面高宽比的增大,车轮侧向刚度呈减小趋势.通过对车轮侧向刚度影响因素的理论及数值分析,可为优化车轮刚度特性及改进车轮结构等方面的研究提供参考.