三维电子光学模拟器的网格自适应研究

根据微波管电子光学系统有限元数值分析的特点,介绍了微波管电子光学系统有限元网格自适应的后验误差估计方法和网格自适应加密策略,并成功地在微波管模拟器套装电子光学模拟器中实现了网格自适应技术。以单阳极无栅电子枪为例,给出了网格自适应方法的计算结果,同时比较了均匀加密与网格自适应加密的计算结果,结果表明:网格自适应加密具有更好的收敛性以及更快的收敛速度,同时也表明提出的网格自适应方法是有效的。     

非结构子网格压力方法抑制爆轰模拟中的砂漏畸变

本文推广包括子网格压力和边粘性的相容流体算法到非结构网格,研制了包括子网格压力和边粘性的非结构网格相容流体程序,对Saltzman活塞问题和平面爆轰问题进行了数值模拟。从数值结果分析可知,包括子网格压力和边粘性的非结构网格相容流体算法能够有效捕捉流体的激波间断,成功抑制虚假涡漩,消除爆轰模拟中的砂漏畸变。     

亚颗粒尺度颗粒群运动三维直接数值模拟

提出一种基于有限元的虚拟区域法,可在亚颗粒尺度上实现对三维颗粒群运动的高效直接数值模拟;基于虚拟区域法的思想将颗粒视为浸入在背景网格中的有限大小区域而非零维点,在有限元方法的离散方程中引入体现颗粒作用的动量方程源项以保证颗粒的刚体运动;给出了三维虚拟区域法的实现方式与数值检验结果,并对管道中的颗粒群实际运动过程进行了直接数值模拟,得到了颗粒群与流场相互作用的非稳态结果。结果表明,虚拟区域法不仅能够处理三维颗粒运动的颗粒边界条件,不需要重新划分网格,而且还可以用于进行多颗粒运动系统的亚颗粒尺度直接数值模拟,最终得到详细的速度场和受力结果。     

圆环在横向冲击荷载作用下的瞬态响应的UL格式有限元数值模拟

本文采用修正的Lagrangian格式(UL格式)有限元中心差分算法,对圆环在横向冲击荷载作用下的瞬态响应进行数值模拟。采用一阶自适应技术,处理冲击接触面和网格失稳现象。具体算例表明了本文处理方法的合理性。     

自适应有限元-离散元算法、ELFEN软件及页岩体积压裂应用

该文介绍流体-固体-断裂耦合分析的自适应有限元（FE）-离散元（DE）算法,引进一款新近基于该方法研发的数值计算软件ELFEN,并将其应用于页岩分段体积压裂的三维数值计算和机理分析。该方法引入有限元应力恢复的超收敛拼片恢复（SPR）法,获得应力的超收敛SPR解,利用SPR解估计常规有限元解的误差,通过裂纹尖端局部区域的自适应网格重划分获得高精度应力解答并得以有效描述裂纹动态扩展,形成分析策略和求解方案。数值算例表明该算法和软件分析流体-固体-断裂耦合作用下单一、多水平井分段体积压裂的可靠性、有效性和实用性。     

复合材料细观结构三维有限元网格模型的建立

提出了针对颗粒夹杂为椭球形状并呈随机分布的多相复合材料的三维有限元网格的建立方法,为复合材料细观结构研究提供了一种全自动的建模工具。引入了以体积为标度的任意两椭球骨料侵入的判别准则,实现了一种三维随机骨料的投放算法;在基于映射法的颗粒表面有限元网格生成算法中通过扫描线布点和局部连接技术较好地解决了网格极化现象;采用改进的三维AFT方法生成基体的四面体网格,并利用AFT特性一次生成所有颗粒夹杂的四面体网格;为进一步的复合材料细观结构与宏观力学性能的多尺度计算打下了基础。最后用几个算例验证了算法的有效性。     

自适应网格方法在Stokes问题形状最优控制中的应用

为了求解流体力学中的形状最优控制问题,本文提出了一种与最优化准则方法相耦合的自适应网格方法.优化的目标是使得流体流动的能量耗散达到最小,状态方程是Stokes问题.本算法可以在减少计算量的情况下,保证流体的界面达到较高的分辨率.最优化算法采用的是非常稳定的经典最优化准则方法,自适应网格的指示函数是通过材料分布的信息得到的.虽然本文只是考虑了Stokes问题,但所得算法可以用来解决很广泛的一类流体动力学中的形状或拓扑最优化问题.     

非定常N-S方程的双重网格数值模拟

本文采用全离散双重网格算法（时间变量采用Eular全隐式格式离散,空间变量采用混合有限元离散）,对非定常Navier-Stokes（N-S）方程进行数值模拟.双重网格算法的基本思想是,首先在粗网格有限元空间X^H上求解一个非线性问题,然后在细网格有限元空间Xh（h＜＜H）上求解一个线性问题.数值实验结果表明：在保持几乎相同精度的前提下,双重网格算法比标准有限元算法节省近一半的计算时间,说明了新算法求解非定常N-S方程的可行性和高效性.     

基于p型超收敛计算的一维有限元自适应分析

基于提高单元阶次的p型超收敛算法,可以在有限元解答基础上求得超收敛解。用该超收敛解代替精确解可以对有限元解答进行可靠的误差估计。对Zienkiewicz网格划分策略进行一定的改进,得到一种更有效的网格划分策略。基于可靠的误差估计和高效的网格划分,可以进行有限元自适应求解。数值试验表明,该文的自适应求解方案能够得到较优的网格和满足误差限的解答。     

含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析

该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案,实现裂纹大小(深度)、位置、数目的模拟.引入变截面Euler-Bernoulli梁的h型有限元网格自适应分析方法,求解含裂纹损伤圆弧曲梁弹性屈曲问题,得到优化的网格和满足预设误差限的高精度屈曲荷载和屈曲模态解答.数值算例表明该算法中网格非均匀加密可适应裂纹损伤引起的屈曲模态...     

Tetrahedral mesh generation in convex primitives

This paper presents a method for generating tetrahedral meshes in three-dimensional primitives. Given a set of closed and convex polyhedra having non-zero volume and some mesh controlling parameters, the polyhedra are automatically split to tetrahedra satisfying the criteria of standard finite element meshes. The algorithm tries to generate elements close to regular tetrahedra by maximizing locally the minimum solid angles associated to a set of a few neighbouring tetrahedra. The input parameters define the size of the tetrahedra and they can be used to increase or decrease the discretization locally. All the new nodes, which are not needed to describe the geometry, are generated automatically.     

A neural network graph partitioning procedure for grid‐based domain decomposition

This paper describes a neural network graph partitioning algorithm which partitions unstructured finite element/volume meshes as a precursor to a parallel domain decomposition solution method. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialize an optimization of the graph partition problem. In practice, a hierarchy of (usually more than two) graphs are used to help obtain the final graph partition. A mean field theorem neural network is used to perform all partition optimization. The partitioning method is applied to graphs derived from unstructured finite element meshes and in this context it can be viewed as a multi‐grid partitioning method. Copyright © 1999 John Wiley & Sons, Ltd.     

基于基面力概念的余能原理任意网格有限元方法

利用基面力概念,给出一种任意形状网格都可以使用的柔度矩阵表达式的具体形式,运用拉格朗日乘子法得到以基面力为基本未知量的余能原理有限元支配方程,提出计算节点位移的表达式,编制出相应的任意网格有限元计算程序。该文对不同形状的单元网格以及畸变网格进行了计算分析,并与理论解和传统的有限元进行了对比和讨论。结果表明:该方法可以适用于任意形状的有限元网格,对网格的畸变不敏感。     

Processing of complexly shaped multiply connected domains in finite element mesh generation

Large number of finite element models in modern materials science and engineering is defined on complexly shaped domains, quite often multiply connected. Generation of quality finite element meshes on such domains, especially in cases when the mesh must be 100% quadrilateral, is highly problematic. This paper describes mathematical fundamentals and practical implementation of a powerful method and algorithm allowing transformation of multiply connected domains of arbitrary geometrical complexity into a set of simple domains; the latter can then be processed by broadly available finite element mesh generators. The developed method was applied to a number of complex geometries, including those arising in analysis of parasitic inductances and capacitances in printed circuit boards. The quality of practical results produced by the method and its programming implementation provide evidence that the algorithm can be applied to other finite element models with various physical backgrounds.     

A new method for finite element transitional mesh generation

In the preparation of finite element meshes, inclusion of transitional blocks is important in order to construct optimal meshes. In this paper, a new method is proposed which is capable of generating quaddominated arbitrary transitional meshes. These meshes are well graded and do not require any mesh smoothening algorithm. The inverse isoparametric mapping combined with an elimination procedure is used to construct transition zones. This new algorithm is described in detail and its efficiency is illustrated with appropriate examples. Different methods available for inverse isoparametric mapping are discussed with their merits and limitations. Many of the existing techniques for inverse isoparametric mapping require the calculation of some special coefficients which may vary with the element type. These techniques lose their clarity and efficiency in the case of three dimensional and higher order two dimensional elements. In this paper, a generalized iterative procedure is proposed to carry out the inverse isoparametric mapping. The computations in this approach are already part of every finite element program based on the isoparametric formulation. Hence implementation of the new algorithm is very simple and straightforward.     

A non‐oscillatory method for spallation studies

This paper introduces a non‐oscillatory method, the finite element flux‐corrected transport (FE‐FCT) method for spallation studies. This method includes the implementation of a one‐dimensional FCT algorithm into a total Lagrangian finite element method. Consequently, the FE‐FCT method can efficiently eliminate fluctuations behind shock wave fronts without smearing them. In multidimensional simulations, the one‐dimensional FCT algorithm is used on each grid line of the structured meshes to correct the corresponding component of nodal velocities separately. The requirement of structured meshes is satisfied by using an implicit function so that arbitrary boundaries of the simulated object can be described. In this paper, the proposed FE‐FCT method is applied in spallation studies. One‐ and two‐dimensional examples show this non‐oscillatory method could be one of the candidates to accurately predict spallation and the spall thickness. Copyright © 2005 John Wiley & Sons, Ltd.     

Automatic mesh generation and adaptation by using contours

A general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing function. The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite element meshes of different element sizes are generated using the available general-purpose mesh generators.^{1, 2} Examples of remeshing for various node spacing functions are given to illustrate that high-quality gradation meshes can be generated automatically without any user's intervention by this simple contour line method.     

Multiple holes,cracks, and inclusions in anisotropic viscoelastic solids

By using the elastic–viscoelastic correspondence principle, the problems with multiple holes, cracks, and inclusions in two-dimensional anisotropic viscoelastic solids are solved for the cases with time-invariant boundaries. Based upon this principle and the existing methods for the problems with anisotropic elastic materials, two different approaches are proposed in this paper. One is concerned with an analytical solution for certain specific cases such as two collinear cracks, collinear periodic cracks, and interaction between inclusion and crack, and the other is a boundary-based finite element method for the general cases with multiple holes, cracks, and inclusions. The former considers only specific cases in infinite domain and can be used as a reference for any other numerical methods, and the latter is applicable to any combination of holes, cracks and inclusions in finite domain, whose number, size and orientation are not restricted. Unlike the conventional finite element method or boundary element method which usually needs very fine meshes to get convergence solutions, in the proposed boundary-based finite element method no meshes are needed along the boundaries of holes, cracks and inclusions. To show the accuracy and efficiency of these two proposed approaches, several representative examples are implemented analytically and numerically, and they are compared with each other or with the solutions obtained by the finite element method.     

一维EEP自适应技术新进展:从线性到非线性

有限元后处理中超收敛计算的EEP(单元能量投影)法以及基于该法的自适应分析方法对线性ODE(常微分方程)问题的求解已经获得了全面成功,也推动了非线性ODE问题自适应求解的研究。经过研究,已经实现了一维有限元自适应分析技术从线性到非线性的跨越,该文意在对这方面的进展作一简要综述与报道。该文提出一种基于EEP法的一维非线性有限元自适应求解方法,其基本思想是通过线性化,将现有的线性问题自适应求解方法直接引入非线性问题求解,而无需单独建立非线性问题的超收敛计算公式和自适应算法,从而构成一个统一的、通用的非线性问题自适应求解算法。该文给出的数值算例表明所提出的算法高效、稳定、通用、可靠,解答可逐点按最大模度量满足用户给定的误差限,可作为先进高效的非线性ODE求解器的核心理论和算法。     

Hierarchical tree‐based finite element mesh generation

Hierarchical grid generation and its use as a basis for finite element mesh generation are considered in this paper. The hierarchical grids are generated by recursive subdivision using quadtrees in two dimensions and octrees in three dimensions. A numbering system for efficient storage of the quadtree grid information is examined, tree traversal techniques are devised for neighbour finding, and accurate boundary representation is considered. It is found that hierarchical grids are straightforward to generate from sets of seeding points which lie along domain boundaries. Quadtree grids are triangularized to provide finite element meshes in two dimensions. Three‐dimensional tetrahedral meshes are generated from octree grids. The meshes can be generated automatically to model complicated geometries with highly irregular boundaries and can be adapted readily at moving boundaries. Examples are given of two‐ and three‐dimensional hierarchical tree‐based finite element meshes and their application to modelling free surface waves. Copyright © 1999 John Wiley & Sons, Ltd.