用边界元方法分析复合材料中的裂纹问题

利用层状材料的广义Klevin基本解，建立了计算三维层状材料中的裂纹边界元方法。采用边界元方法中的多区域方法和能反映均匀介质中裂纹尖端应力场和位移场特征的面力奇异单元。裂纹的应力强度因子由裂纹面上的位移经插值计算得到。算例分析表明，本文建议的方法可以获得较高的计算精度。     

一种XFEM断裂分析的裂尖单元新型改进函数

提出了一种适用于裂尖改进单元的新型改进函数, 基于三角变换的方法, 保留裂纹尖端场的应力奇异性和裂纹上、下表面的位移不连续性, 将常规扩展有限元法裂尖改进单元的4 项改进函数缩减为2 项, 裂尖改进单元的结点由常规的8 个改进自由度减少为4 个. 采用2 个正交的水平集函数表征材料内部裂纹面, 详细阐述了改进单元类型的判别方法, 给出一种改进单元的分区域积分方案. 最后, 若干断裂力学问题经典算例的数值计算结果表明:建议的裂尖改进函数具有较高的数值精度, 该方法是十分有效的.     

势问题的重构核粒子边界无单元法

将重构核粒子法和势问题的边界积分方程方法结合,提出了势问题的重构核粒子边界无单元法. 推导了势问题的重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核粒子边界无单元法的离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位势的积分公式. 重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点的精确值,所以该方法具有更高的精度. 最后给出了数值算例,验证了所提方法的有效性和正确性. }      

一种处理弹性动力边界元法中奇异积分的方法

利用边界元法求解瞬态弹性动力学问题时,时域基本解函数的分段连续性和奇异性为该问题的求解带来很大的困难。为了解决时域基本解中的奇异性问题,本文依据柯西主值的定义,对经过时间解析积分之后的时域基本解进行奇异值分解,将其分成奇异和正则积分两部分;其中正则部分可通过采用常规高斯积分方法来计算,而奇异部分具有简单的形式,可以利用解析积分计算。经过上述操作之后,就可以达到直接消除时域基本解中奇异积分的目的。和传统方法相比,本文方法并不依赖静力学基本解来消除奇异性,是一种直接求解方法。最后给定两个数值算例来验证本文提出方法的正确性和可行性,结果表明使用本文算法可以解决弹性动力学边界积分方程中的奇异性问题。     

等参管单元及其在热传导问题边界元法中的应用Isoparametric tube elements and their application in heat conduction BEM analysis

采用边界元法（BEM ）求解实际工程问题时,很大一部分误差来自于离散误差。为此,本文基于Lagrange插值原理,提出了一种三维等参管单元边界元算法,该单元能很好地模拟管状结构的几何外形并对物理量进行高阶插值,大大地消除了离散误差。另外,当在边界元法中使用等参管单元时,提出了一种在等参平面内消除积分奇异性的方法。算例表明,本文算法具有划分网格少,求解精度高的优点。     

集成单元边界元法及其在主动冷却热防护系统分析中的应用

随着高超声速飞行器的快速发展,飞行器及发动机所面临的热防护压力越来越大. 传统的被动热防护系统已很难满足设计要求,因此主动冷却热防护系统受到了越来越多的关注. 主动冷却热防护系统因为管道密布、结构复杂,传统的分析方法需要花费大量的精力和时间来建模和计算分析. 针对管道阵列排布的主动冷却系统,提出了一种用边界元法求解空间周期性结构的集成单元法,并将其用来分析具有冷却通道的热防护系统的传热与受力变形问题. 此方法求解空间周期性结构问题,仅需要针对一个胞元建立边界元胞元方程,并由其形成由指定胞元数组成的集成单元,然后由集成单元组集成总体系统方程组. 提出的集成单元法既有常规子结构法的消元思想,又有传统有限单元、边界单元易于组集的特征,便于大型空间周期性结构的快速分析. 由于集成单元的系数矩阵只需形成一次,且最终方程只含边界节点未知量,计算效率显著提高. 论文最后用功能梯度平板和主动冷却燃烧室算例验证了本文所述算法的正确性和计算效率.      

裂纹扩展独立于网格的一种有限元单元子划分方法

提出了一种有限元模拟裂纹扩展的单元子划分结合子结构的方法.该方法中,裂纹可以进入或穿过一个单元,或沿单元的边界扩展,因此裂纹可以沿任意路径扩展而不受初始网格的限制.对上述几类包含裂纹的单元按照裂纹的路径进行子划分,覆盖一条裂纹的所有子划分单元就组成了一个子结构,子结构规模随裂纹的扩展而增大.子结构中因单元子划分而新增的结点自由度,通过自由度的凝聚用初始网格结点的自由度表示,因此结构整体分析的总自由度不变.以上述方法为基础建立了裂纹萌生和扩展的准则.用论文的方法分析了单(双)材料无限大平面中心(界面)裂纹的裂尖场,验证了论文方法的精度,并模拟了颗粒复合材料中微裂纹在颗粒、基体和界面中逐步扩展的过程,考核了论文方法对复杂裂纹扩展问题模拟的适用性.     

边界元法在求解复合材料力学问题中的应用

本文讨论了边界元法在求解复合材料的微观力学、宏观力学和结构力学问题中的应用,并指出边界元法用于分析复合材料及其结构的力学问题的优点和局限性。      

三维有限裂纹体分析

基于胡海昌教授提出的一类不含强奇异积分的新型面力边界积分方程,针对含平面裂纹三维有限体问题给出了的数值分析和半解析数值分析裂式.文中对含圆裂纹或裂纹系的厚板、圆柱,以及含垂直于表面的椭圆裂纹的矩形板等有关问题进行了具体求解,求得了相应的应力强度因子.将文中计算结果与已有结果比较表明,该方法具有较高的精度,而计算量较小.     

二维正交各向异性位势问题的高阶单元快速多极边界元法

研制了一种适用于二维正交各向异性位势问题的高阶单元(线性单元和二次单元)快速多极边界元法.在快速多极边界元法中,源点对于远场区域的积分采用快速多极展开式计算,而对于近场区域的积分则直接进行计算.高阶单元的使用使得近场积分,尤其是奇异积分和几乎奇异积分的计算更加复杂.通过引入复数表达对其进行简化,若边界采用线性单元插值,...     

The analysis of crack problems with non-local elasticity

IntroductionTheclassicalconhnuummechanicshasbeenusedtosolvemanyproblemsinmacrofracturemechanics,butencountersdifficulheswhentheeffectofITilcrocharacteristicdimensionshouldbetakenintoaccount.Thestressfieldverynearthecracktipisstillnotclear.Somephenomenaofshortcrackscannotbeexplained["']andsomemechanismoffracturehasnotbeensolvedyet.Thenon-localelashcitytheoryseemsattractivetotheseproblems.Thetheoryofnon-localelasticity,establishedanddevelopedbyEringenetal[3),connectstheclassicalcontinuummechan…     

Mathematical problems in the integral-transformation method of dynamic crack

In the investigation on fracture mechanics, the potential function was introduced,and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied.After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility. A model for example is taken to explain the problems existing in initial deriving process of the integral-transformation method of dynamic crack.     

A higher-order boundary element method for three-dimensional potential problems

A method of eliminating the singularities involved in boundary element methods for three-dimensional potential problems is presented and the non-singular expressions of integrals on an element on which the singular point is situated are given for linear and quadratic interpolation functions. Numerical examples are compared with analytical solutions to show that the higher-order interpolations have better precision.     

NEW BOUNDARY ELEMENT METHOD FOR TORSION PROBLEMS OF CYLINDER WITH CURVILINEAR CRACKS

The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.     

New type of dual bem and Green's-function-library strategy for fracture analysis in complex structures

A new type of dual boundary integral equations (DBIE) is presented first, through which, a smaller system of equations needs to be solved in fracture analysis. Then a non-conforming crack tip element in two-dimensional problems is proposed. The exact formula for the hypersingular integral over the non-conforming crack tip element is given next. By virtue of Green's-function-library strategy, a series of stress intensity factors (SIF) of different crack orientations, locations and/or sizes in a complicated structure can be obtained easily and efficiently. Finally, several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed. Partially supported by the Aeronautical Science Foundation of China (No. 99C53026)     

A triangular quasi-conforming finite element for transient dynamic analysis

A type of 3 node triangular element is constructed by the Quasi-conforming method, which may be used to solve the equation of a type of inverse problem of wave propagation after Laplace transformation Δu−A ² u=0. The strains in the element are approximated by an exponential function and the string-net function between neighbouring elements is approximated by one dimensional general solution of the equation. Furthermore the strain field satisfies the equation, and therefore in the derivation of the element formulation, no shape function is needed. In this sense, it is a kind of hybrid element. Compared with the ordinary linear triangular element, the new one features higher precision with coarse meshes. Some numerical tests are presented. The project is supported by the National Natural Science Foundation of China.     

Boundary element analysis of contact problems using artificial boundary node approach

An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.     

模拟相变问题的精细积分边界元法

将精细积分边界元法和界面追踪法相结合求解相变问题。因为边界元法只需要将待求解空间域的边界离散,方便连续追踪移动界面位置和重构网格,所以边界元法适合应用于移动边界问题的模拟。首先,利用精细积分边界元法在固相区域和液相区域分别求解相应的瞬态热传导控制方程,从而求得温度场和边界热流密度。然后,根据固-液相变界面上的能量平衡方程,利用热流密度求得相变界面的移动速度,再采用界面追踪法预测移动相变界面的位置变化。最后,给出了几个数值算例,并通过与参考解的对比验证本文方法的准确性。     

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。