基于重叠划分的自由网格四边形单元计算方法

提出了一种基于重叠划分的自由网格四边形单元计算方法。这一方法将四边形单元引入到自由网格计算方法中，不仅提高了计算的精度，同时还保留了自由网格计算方法的特点。方法首先对分析域内自动生成的每一个节点建立一套临时三角形单元，利用这些临时三角形单元组合生成四边形单元，以节点为单位进行计算。由于各矩阵的计算与组集均以节点为中心进行处理，因而特别适合于并行计算环境。在详细介绍自由网格四边形单元计算方法的基础上，利用数值算例证实了这一方法改善计算精度方面的有效性。     

基于面积坐标与B网方法的四边形样条单元

传统等参元方法中, S型等参元完备阶较低,对网格畸变敏感, L型等参元具有高阶完备性但需要使用内部节点. 另外,由于引入等参变换, 采用数值积分可能导致总刚度矩阵出现奇异性.利用三角形面积坐标与B网方法建立了一类平面四边形的样条单元函数,它们的特点是满足协调条件, 克服网格畸变敏感性.其中8节点和12节点单元分别为2次和3次样条函数,对直角坐标分别具有二阶和三阶完备性, 高于相同节点的S型等参元.通过算例测试了这些样条单元, 并与等参元和其它四边形单元比较,数值结果显示了它们的高精度和有效性.      

无限大基体中双圆形夹杂的应力干涉问题研究

建立了一种新型圆形夹杂单元,用于考察y向拉伸情况下无限大板中双圆形夹杂互相干涉问题,分析材质、位置关系与间距等对夹杂应力场的影响.算例考虑了两夹杂连线与Z轴的夹角φ2分别为0°,45°和90°三种情况,计算结果表明:(1)该模型能够用较少的单元数获得令人满意的计算结果,尤其适用于多夹杂的应力分析;(2)夹杂/基体刚度比k不同时,夹杂/基体界面上的周向应力的最大值与最小值的出现位置差异可能很大;(3)两夹杂的距离越近,夹杂之间基体的正应力σ_y会急剧上升或下降,具体变化趋势取决于k和φ_(21);(4)特定φ_(21)的情况下,夹杂/基体刚度比k使夹杂之间基体的正应力σ_y单调变化.     

基于扩展有限元的结构内部缺陷(夹杂)的反演分析模型

传统的结构检测方法一般需要钻孔取样,对结构本身有一定的破坏作用,而无损检测方法在检测过程中不破坏结构本身,这项技术的重要性日益显著. 结合扩展有限元法和人工蜂群智能优化算法的优点,建立了结构内部缺陷(夹杂)的反演分析模型,为结构的无损检测技术提供了一条新的途径.扩展有限元法通过引入非连续位移模式可以在不重新划分网格的情况下通过改变水平集函数反映缺陷(夹杂)的位置及大小,避免了反演分析每次迭代过程中的网格重剖分,人工蜂群智能优化算法在每次迭代中都采用全局和局部搜索,找到最优解的概率大大增加并可很好地避免局部最优,因此,扩展有限元法与人工蜂群智能优化算法的结合有效地减少了反演分析的计算工作量. 通过若干算例的分析表明:建立的反演分析模型能准确地探测结构内部存在的单个缺陷(夹杂).      

椭圆类夹杂分析的杂交应力有限元方法

论文给出了一种分析椭圆类夹杂周边应力场的新型杂交应力有限元方法.基于弹性力学中平面问题的Muskhelishvili复势方法,应用保角变换映射技术,以Laurent级数和Faber级数为工具,借助Hellinger-Reissner原理构建一个能够反映椭圆类夹杂周边弹性现象同时包含椭圆夹杂的多边形超级单元.将该超级单元与标准的4结点杂交应力单元耦合在一起即可建立一种分析椭圆类夹杂周边弹性场的新型特殊杂交应力有限元方法.文中考核算例表明:该文方法不但使用简单、有效,而且精度高、单元少.作为论文方法的一个拓展应用,文章最后给出了一个分析含二个椭圆夹杂无限大各向同性板在远场均布载荷作用下椭圆夹杂周边弹性场的算例,并讨论了椭圆夹杂间距和弹性刚度比对应力集中系数的影响.     

状态向量的扩展有限元方法研究

利用哈密顿正则方程的半解析法计算单元位移场和应力场,可以得到精度比较高的解.但此半解析法在计算应力尖峰区域时,该区域要细化网格.当裂纹扩展时,又要重新生成刚度矩阵进行求解,导致求解效率降低.利用扩展有限元处理裂纹的不连续性,当裂纹扩展时可以避免网格的重构.为充分利用状态向量方程和扩展有限元的优势,该文将两者结合起来分析材料的断裂问题:计算应力强度因子和模拟裂纹扩展.最后通过算例分析,验证了该文提出方案的可行性.     

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.     

求解含钝裂纹体应力场的扩展单元方法

本文基于钝裂纹端部位移场的渐近解和等参元构造方法,开发了一种新的适合钝裂纹端部应力场计算的扩展单元法,为了消除不同单元间的位移不协调又在扩展单元的基础上提出过渡单元.和常规的等参元相比,扩展单元除了以节点位移为待求未知量外,它们额外增加了Ⅰ型和Ⅱ型广义应力强度因子作为未知量.根据这个理论我们编制了有限元的程序并计算了算例,算例表明,在网格较大的情况下,与常规等参元计算方案相比,扩展单元和过渡单元法更好地接近理论值,它具有计算精度高、减少缺陷附近的单元数量和计算时间等优点.     

具有单元分裂功能的间断有限元方法

介绍一种能够模拟材料开裂过程的有限元方法,该方法引入单元分裂和界面分离技术,结合具体的破坏准则,模拟材料变形中的破坏,同时还可以方便地处理材料中任意分布的界面结构．以三点弯曲实验为例,通过数值模拟结果和实验数据的比较,验证了该方法的适用性．     

基于单元破裂的岩石裂纹扩展模拟方法

传统离散元方法在处理破裂问题时, 采用界面上的准则进行判断, 裂纹只能沿着单元边界扩展. 当物理问题存在宏观或微观裂隙时, 在界面上应用准则具有其合理性; 而裂纹沿着单元边界扩展, 使得裂纹路径受网格影响较大, 扩展方向受到限制. 针对上述情况, 可以基于单元破裂的方式, 构建连续- 非连续单元法, 并应用于岩石裂纹扩展问题的模拟. 该方法在连续计算时, 将单元离散为具有物理意义的弹簧系统, 在局部坐标系下由弹簧特征长度、面积求解单元变形和应力, 通过更新局部坐标系和弹簧特征量, 可进一步计算块体大位移、大转动, 连续问题计算结果与有限元一致, 同时提高了计算效率. 在此基础上, 引入最大拉应力与莫尔—库伦的复合准则, 判断单元破裂状态和破裂方向, 并采用局部块体切割的方式, 在单元内形成初始裂纹. 裂纹两侧相应增加新的计算节点, 同时引入内聚力模型描述裂纹两侧的法向、切向作用与张开度及滑移变形之间的关系. 按此方式, 裂纹尖端处的扩展路径可穿过单元内部和单元边界, 在扩展方向的选取上更为准确. 最后, 通过三点弯曲梁、单切口平板拉伸、双切口试样等典型数值试验, 模拟裂纹在拉伸、压剪等各种应力状态下的扩展问题, 并对岩石单轴压缩试验的破坏过程进行模拟, 分析裂纹形成与应力—应变曲线各阶段之间的对应关系. 结果表明: 连续—非连续单元法通过单元内部破裂的方式, 可以显示模拟裂纹萌生、扩展、贯通直至形成宏观裂缝的过程.      

基于扩展有限元法的裂尖场精度研究

扩展有限元方法基于单元分解的基本思想,通过引入位移加强函数来表征裂纹的不连续性和裂尖的奇异性。在裂尖加强单元与常规单元之间有一层混合单元,当对裂尖特定区域进行加强时,混合单元个数相应增加,混合单元个数与计算精度存在一定联系。本文提出一种正方形裂尖加强区域的选择方式,可得到较单个加强和圆形加强精度更高、更稳定的计算结果。对于不同长度的裂纹,表征裂尖场奇异性所需的裂尖加强范围存在较大差异,以正方形裂尖加强方式进行计算,得到了不同裂纹长度下最优的加强尺寸。     

基于扩展有限元法的混凝土细观断裂破坏过程模拟

扩展有限元法（XFEM）是分析不连续力学问题（特别是断裂问题）的一种有效的数值方法。在常规的有限元位移模式中,基于单位分解的思想加入一个跳跃函数和渐进缝尖位移场来对不连续体附近的节点自由度进行局部加强,从而反映了位移的不连续性。介绍了扩展有限元的基本原理,给出了扩展有限元进行混凝土开裂及裂纹扩展的分析方法,最后采用扩展有限元法模拟了湿筛混凝土单轴拉伸作用下及WinklerL-型混凝土板的细观断裂破坏过程。分析了混凝土裂纹萌生、扩展的过程及破坏形态,数值结果与实验结果吻合良好。研究表明：扩展有限元法通过特定的位移模式,使裂纹两侧不连续位移场的表达独立于网格划分,能有效地模拟混凝土材料细观断裂破坏过程。     

A modified finite element method for solving the time-dependent,incompressible Navier-Stokes equations. Part 1: Theory

Beginning with the Galerkin finite element method and the simplest appropriate isoparametric element for modelling the Navier-Stokes equations, the spatial approximation is modified in two ways in the interest of cost-effectiveness: the mass matrix is ‘lumped’ and all coefficient matrices are generated via 1-point quadrature. After appending an hour-glass correction term to the diffusion matrices, the modified semi-discretized equations are integrated in time using the forward (explicit) Euler method in a special way to compensate for that portion of the time truncation error which is intolerable for advection-dominated flows. The scheme is completed by the introduction of a subcycling strategy that permits less frequent updates of the pressure field with little loss of accuracy. These techniques are described and analysed in some detail, and in Part 2 (Applications), the resulting code is demonstrated on three sample problems: steady flow in a lid-driven cavity at Re ≤ 10,000, flow past a circular cylinder at Re ≤ 400, and the simulation of a heavy gas release over complex topography.     

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     

分数阶导数粘弹性模型的有限元法

在分析分数阶导数三元件模型理论的基础上,把分数阶导数三元件模型引入有限元模型中,推导出具有分数阶导数三元件本构关系的粘弹性结构动力学有限元格式。同时,应用分数阶导数型粘弹性结构动力学方程的数值算法求解了该有限元格式的数值解。并以二维沥青路面结构为例进行了路面动态粘弹性响应分析。算例分析表明,该方法能够正确有效地进行路面动态粘弹性分析。     

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有限单元法在航空航天领域中应用极其广泛．航空航天专业有限单元法课程应针对其课程特 点而开设,重构课程体系,注重理论联系实际,将教学重心从以往的理论教学转变为应用教 学．文中还给出了在航空航天结构有限单元法教学中应涉及的几个实例．     

Boundary element analysis of interaction between an elastic rectangular inclusion and a crack

The interaction between an elastic rectangular inclusion and a kinked crack inan infinite elastic body was considered by using boundary element method. The new complexboundary integral equations were derived. By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically. Only one complex boundaryintegral equation was obtained on interface and involves only singularity of order l/ r. Toverify the validity and effectiveness of the present boundary element method, some typicalexamples were calculated. The obtained results show that the crack stress intensity factorsdecrease as the shear modulus of inclusion increases. Thus, the crack propagation is easiernear a softer inclusion and the harder inclusion is helpful for crack arrest.     

Dealing with extremely large deformation by Nearest-Nodes FEM with algorithm for updating element connectivity

In the recently developed Nearest-Nodes Finite Element Method (NN-FEM), elements are mainly used for numerical integration; while shape functions are constructed in a similar way as in meshless methods. Based on this strategy, NN-FEM inherits major merits from both the classical Finite Element Method and meshless methods. One of them is that NN-FEM is nearly not affected by element distortion. So NN-FEM is more efficient than the classical FEM on dealing with large deformation problems. Nevertheless, NN-FEM still has a requirement on finite element meshes, that is, elements in a mesh are required not to overlap or penetrate to each other, to avoid difficulty in numerical integration. To eliminate overlapped elements, NN-FEM is supplemented with an algorithm for updating element connectivity. With this supplement, NN-FEM is able to deal with extremely large deformation. In updating element connectivity, element nodes are kept not changed and all information associated with nodes are not touched. Therefore, there is no need to transfer solution data, and error introduced by solution transfer is avoided.     

Comparison between the traction and pressure-imposed boundary conditions in finite element flow analysis

A formulation is developed to impose pressure-prescribed boundary conditions in the penalty finite element method. Some numerical experiments for the Poiseuille flow problem are performed to compare it with the conventional traction-prescribed boundary condition. Also the incorrectness of the traction-free outlet boundary condition for contained-flows is studied with explanatory numerical examples. Discussion is focused on the inlet and outlet boundary conditions to simulate fully developed flows. Finally, the three-dimensional flow in a bifurcated pipe is analysed with the proposed formulation.     

Simulation of a soil loosening process by means of the modified distinct element method

We apply the Distinct Element Method (DEM) to analyze the dynamic behavior of soil. However, the conventional DEM model for calculation of contact forces between elements has some problems; for example, the movement of elements is too discrete to simulate real soil particle movement. Therefore, we modify the model to solve the difficulties. To investigate the validity of the modified model, we conduct an experiment in which soil is cut with a pendulum-typeblade, and simulate the soil loosening process with the modified DEM model. This paper presents details of the experimental apparatus and the comparison of soil behavior and energy absorption between the simulation and the experiment. Some characteristic phenomena of the experiment are reproduced in the simulation giving us confidence that the modified model is better than the conventional model for the simulation of soil behavior.