一种快速有限单元法及其在三维磁场计算机中的应用

针对大容量三维磁场的计算机模拟提出了一种快速有限单元法，通过用索引的方式进行刚度矩阵的计算与存储，大大节省了计算所需内存，采用超松驰迭代法进行求解，在大容量方程组的求解上大大快于上下三角（LU）分解法，提高了计算容量和计算速度，并成功地应用于三维偏转磁场的模拟计算。     

螺旋线行波管的时域粒子模拟研究

基于粒子模拟技术研究了螺旋线行波管的时域非线性理论,慢波结构中的场通过螺旋带模型求解得到,并考虑了夹持杆和屏蔽桶的影响,推导得到了注-波互作用的动理学方程;聚焦磁场可以是直流磁场也可以是周期永磁场;用泊松方程求解得到空间电荷场;注-波互作用方程用MacCormack的差分格式进行计算。给出了时域计算得到的瞬态特性,并与基于一维Christine及三维Christine理论的计算结果进行了比较。     

横向稳态磁场作用下微束等离子电弧数值分析

为分析外加横向稳态磁场作用下电弧特性与电弧对工件热、力输入的变化规律,本文建立了微束等离子电弧三维模型,将外加磁场简化为背景场添加至模型,使用有限元分析软件COMSOL进行求解计算.结果表明:外加横向稳态磁场作用下,喷嘴内部各项特性均未发生较大变化,喷嘴下方电弧等离子体在洛伦兹力的作用下向x负方向移动,电弧温度、等离子...     

可视化技术在三维磁场分析软件前后处理中的应用

面向对象技术、可视化技术及人机交互技术等相结合，开发了用于三维磁场计算的积分方程法仿真软件。该软件有可视化的前后处理程序，并且它还可以通过IGES文件格式同常用的三维CAD软件UG—Ⅱ或Pro/E等接口。在前处理中通过交互式技术使用户能够方便、快捷的建立求解模型，在后处理中能够将计算结果以图形方式直观地显示。     

用于偏转线圈三维磁场计算的谐波表面磁荷法

将三维磁场计算的表面磁荷法和空间谐波展开技术相结合 ,提出了一种用于偏转线圈磁场计算的谐波表面磁荷法。利用空间谐波的正交性 ,导出了与铁芯表面感应的磁荷各次谐波一一对应的磁场谐波。根据铁芯表面的法向磁场关系 ,建立各次磁荷谐波的积分方程 ,并进行了离散化。此方法将三维问题简化为一维积分方程问题 ,可以处理铁芯磁导率为有限值及铁芯与线匝间具有任意间隙的情况 ,具有较大的普遍适用性。用此方法计算了一个偏转线圈的例子 ,取得了较好的结果。     

两种不同铁芯结构纵磁真空灭弧室触头三维磁场对比分析

本文建立了两种不同铁芯结构的纵向磁场真空灭弧室触头三维模型,一种铁芯为带有断口的环状结构,另一种是由12个柱状铁芯圆周方向排列的结构,采用有限元分析方法对两种结构的三维模型进行仿真计算,分析对比两种铁芯结构对电流峰值时刻纵向磁场和电流过零时剩余磁场以及磁场滞后时间的影响,计算的过程中考虑到了涡流的影响。从仿真结果中可以得到以下结论:1.电流峰值时环状铁芯结构产生的纵向磁场大于柱状铁芯结构,但柱状铁芯结构产生的纵向磁场比环状铁芯结构的均匀;2.电流过零时两种铁芯结构的剩余磁场分布相似,但环状铁芯结构的剩余纵向磁场大于柱状铁芯结构;3.柱状铁芯结构的磁场滞后时间要小于环状铁芯结构,电流过零时剩余磁场强的区域对应的磁场滞后时间也大。     

三维有限元并行EBE方法

采用Jacobi预处理,推导了基于EBE方法的预处理共轭梯度算法,给出了有限元EBE方法在分布存储并行机上的计算过程,可以实现整个三维有限元计算过程的并行化。编制了三维有限元求解的PFEM(ParallelFiniteElementMethod)程序,并在网络机群系统上实现。采用矩形截面悬臂梁的算例,对PFEM程序进行了数值测试,对串行计算和并行计算的效率进行了分析,最后将PFEM程序应用于二滩拱坝-地基系统的三维有限元数值计算中。结果表明,三维有限元EBE算法在求解过程中不需要集成整体刚度矩阵,有效地减少了对内存的需求,具有很好的并行性,可以有效地进行三维复杂结构的大规模数值分析。     

强磁体结构的磁场和应力同步分析方法

在强磁体结构中，电磁力是主要载荷。由于磁场计算和结构分析属不同学科，这两部分研究一般都是孤立地、分别进行的。本文指出了这样研究的弊病，提出了磁场和应力同步分析的方法。并以中国ＨＬ－１托卡马克磁体为例，采用有限元应力分析和三维磁场计算同步进行的方法，得到了托卡马克环向场线圈的磁体力、应力和变形分布。     

铸造材料伸缩尾翼气动载荷下接触问题的分析与研究

采用有限元技术,应用MSC仿真软件分析铸造材料伸缩结构尾翼在弹道飞行过程中气动载荷矩阵作用下的接触应力问题.通过建立计算模型,施加边界条件及启动接触非线性求解器进行求解,得到尾翼三维结构下的位移和应力情况,该种MD Nastran隐式非线性求解器SOL600计算方法能够充分模拟实际三维结构的接触问题.     

板式电涡流阻尼器有限元仿真与参数优化

为了实现板式电涡流阻尼器的精确、高效和优化设计,首先以某一电涡流调谐质量阻尼器为计算模型,验证了采用三维电磁场有限元稳态分析方法计算板式电涡流阻尼器阻尼系数的准确性。利用三维磁场有限元稳态分析法,分析了板式电涡流阻尼器的各设计参数对阻尼比的影响。结果表明,三维磁场有限元稳态分析方法能够准确计算板式电涡流阻尼器的阻尼系数;导体板厚度、导磁钢板厚度、永磁体间距、空气间隙和永磁体的排列方式对板式电涡流阻尼器的阻尼性能影响显著,在设计中应综合考虑。     

New formulation of the Green element method to maintain its second-order accuracy in 2D/3D

The Green element method (GEM) is a powerful technique for solving nonlinear boundary value problems. Derived from the boundary element method (BEM), over the meshes of the finite element method (FEM), the GEM combines the second-order accuracy of the BEM with the efficiency and versatility of the FEM.The high accuracy of the GEM, resulting from the direct representation of normal fluxes as unknowns, comes at the price of very large matrices for problems in 2D and 3D domains. The reason for this is a larger number of inter-element boundaries connected to each internal node, yielding the same number of the normal fluxes to be determined. The currently available technique to avoid this problem approximates the normal fluxes by differentiating the potential estimates within each element. Although this approach produces much smaller matrices, the overall accuracy of the GEM is sacrificed.The first of the two techniques proposed in this work redefines the present approach of approximating fluxes by considering more elements sharing each internal node. Numerical tests on the potential field exp(x+y) show an increase in accuracy by two orders of magnitude.The second approach is a reformulation of the standard GEM in terms of the flux vector, replacing its normal component. The original accuracy of the GEM is preserved while the number of unknowns is reduced as many as ten-times in the case of a mesh consisting of tetrahedrons. The additional benefit of this novel technique is the fact that the entire flux field is a mere by-product of the basic procedure for determining the unspecified boundary values.     

基于单胞数字化模型的复合材料本构关系三维数值模拟

在渐进均匀化理论基础上, 建立了基于单胞数字化模型的复合材料宏观等效弹性性能的三维数值分析方法(DCB-FEA) 。该方法采用三维光栅化技术将三维单胞模型转化为三维光栅图形(数字化模型) , 并将光栅图形直接转化为三维有限元求解网格。产生的离散单元具有相同的几何尺寸和规则的形状, 单元刚度矩阵的数量将减少为单胞材料的个数。此外, 单胞数字化模型仅需记录每个离散单元的材料种类, 其他参数如单元节点编号、节点坐标等均可在求解过程中自动生成, 周期性边界条件也可以自动施加。随着分辨率的提高, 单胞数字化模型将产生更多数量的单元, 特别是对于三维单胞模型, 集成整体刚度矩阵时需要大量的计算机内存。采用基于Element-by-element 策略的预处理共轭梯度法( EBE- PCG) , 有限元方程的求解在单元级上进行, 避免了整体刚度矩阵的集成。通过对单向纤维增强复合材料的线弹性本构关系的数值模拟, 表明该方法可得到较为准确的复合材料等效模量。      

3D mass-redistributed finite element method in structural–acoustic interaction problems

A 2D mass-redistributed finite element method (MR-FEM) for pure acoustic problems was recently proposed to reduce the dispersion error. In this paper, the 3D MR-FEM is further developed to solve more complicated structural–acoustic interaction problems. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and MR-FEM is applied in acoustic domain. The global equations of structural–acoustic interaction problems are then established by coupling the MR-FEM for the acoustic domain and the edge-based smoothed finite element method for the structure. The perfect balance between the mass matrix and stiffness matrix is able to improve the accuracy of the acoustic domain significantly. The gradient smoothing technique used in the structural domain can provide a proper softening effect to the “overly-stiff” FEM model. A number of numerical examples have demonstrated the effectiveness of the mass-redistributed method with smoothed strain.     

New development in extended finite element modeling of large elasto‐plastic deformations

This paper presents new achievements in the extended finite element modeling of large elasto‐plastic deformation in solid problems. The computational technique is presented based on the extended finite element method (X‐FEM) coupled with the Lagrangian formulation in order to model arbitrary interfaces in large deformations. In X‐FEM, the material interfaces are represented independently of element boundaries, and the process is accomplished by partitioning the domain with some triangular sub‐elements whose Gauss points are used for integration of the domain of elements. The large elasto‐plastic deformation formulation is employed within the X‐FEM framework to simulate the non‐linear behavior of materials. The interface between two bodies is modeled by using the X‐FEM technique and applying the Heaviside‐ and level‐set‐based enrichment functions. Finally, several numerical examples are analyzed, including arbitrary material interfaces, to demonstrate the efficiency of the X‐FEM technique in large plasticity deformations. Copyright © 2008 John Wiley & Sons, Ltd.     

一种高效的FE-PSBFE耦合方法及在岩土工程弹塑性分析中的应用

针对复杂岩土工程结构建模困难、耗时费力的难题,结合八叉树网格离散技术,对网格中的六面体采用等参单元,对于非六面体采用多面体比例边界有限单元（PSBFE）,建立了一种快速、高效的FE-PSBFE弹塑性耦合数值分析方法。采用实现的PSBFE对标准土石坝进行数值模拟,验证了其正确性和计算精度;通过典型复杂心墙坝对提出FE-PSBFE耦合方法的灵活性、通用性和高效性进行了研究,研究结果表明:与传统FEM相比,该耦合方法可大幅加速模型前处理进程,解决了复杂三维空间河谷形状、水平分层填筑和材料分区导致的网格剖分难题,几十万单元的网格划分一般仅需几分钟;与PSBFE相比,显著提高了岩土结构弹塑性分析的效率,FE-PSBFE可减少超过80%的求解时间。FE-PSBFE耦合方法对其他复杂几何条件的工程问题也具有良好的实用性,为快速精细化抗震分析提供了技术手段。     

An Adaptive Fast Multipole Boundary Element Method for Three-dimensional Potential Problems

An adaptive fast multipole boundary element method (FMBEM) for general three-dimensional (3-D) potential problems is presented in this paper. This adaptive FMBEM uses an adaptive tree structure that can balance the multipole to local translations (M2L) and the direct evaluations of the near-field integrals, and thus can reduce the number of the more costly direct evaluations. Furthermore, the coefficients used in the preconditioner for the iterative solver (GMRES) are stored and used repeatedly in the direct evaluations of the near-field contributions. In this way, the computational efficiency of the adaptive FMBEM is improved significantly. The adaptive FMBEM can be applied to both the original FMBEM formulation and the new FMBEM with diagonal translations. Several numerical examples are presented to demonstrate the efficiency and accuracy of the adaptive FMBEM for studying large-scale 3-D potential problems. The adaptive FMBEM is found to be about 50% faster than the non-adaptive version of the new FMBEM in solving the model (with 558,000 elements) for porous materials studied in this paper. The computational efficiencies and accuracies of the FMBEM as compared with the finite element method (FEM) are also studied using a heat-sink model. It is found that the adaptive FMBEM is especially advantageous in modeling problems with complicated domains for which free meshes with much more finite elements would be needed with the FEM.     

附加约束阻尼层的复合材料梁单元建模分析

复合材料空心圆截面梁是桁架和刚架结构中大量采用的常用构件，而实践证明约束阻尼层能有效改善复合材料空心圆截面梁的动力学特性，但传统的约束阻尼层结构有限元计算方法需要大量的单元，这给大型复杂结构的计算带来了巨大的困难。本文采用Timoshenko梁假定。建立了一类附加约束阻尼层复合材料空心圆截面梁弯曲的数学模型。应用Hamilton原理。采用三节点高次梁单元对构件进行离散化。建立了附加约束阻尼层复合材料空心圆截面梁的梁单元。同传统的锥壳单元相比，该方法极大地减少了计算时间。用实验验证了本文计算结果的正确性。同时也分析了约束层厚度对损耗因子的影响。     

A quasi‐static crack growth simulation based on the singular ES‐FEM

In the edge‐based smoothed finite element method (ES‐FEM), one needs only the assumed displacement values (not the derivatives) on the boundary of the edge‐based smoothing domains to compute the stiffness matrix of the system. Adopting this important feature, a five‐node crack‐tip element is employed in this paper to produce a proper stress singularity near the crack tip based on a basic mesh of linear triangular elements that can be generated automatically for problems with complicated geometries. The singular ES‐FEM is then formulated and used to simulate the crack propagation in various settings, using a largely coarse mesh with a few layers of fine mesh near the crack tip. The results demonstrate that the singular ES‐FEM is much more accurate than X‐FEM and the existing FEM. Moreover, the excellent agreement between numerical results and the reference observations shows that the singular ES‐FEM offers an efficient and high‐quality solution for crack propagation problems. Copyright © 2011 John Wiley & Sons, Ltd.     

A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements

This paper presents a novel face‐based smoothed finite element method (FS‐FEM) to improve the accuracy of the finite element method (FEM) for three‐dimensional (3D) problems. The FS‐FEM uses 4‐node tetrahedral elements that can be generated automatically for complicated domains. In the FS‐FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements. The results demonstrated that the FS‐FEM is significantly more accurate than the FEM using tetrahedral elements for both linear and geometrically non‐linear solid mechanics problems. In addition, a novel domain‐based selective scheme is proposed leading to a combined FS/NS‐FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The implementation of the FS‐FEM is straightforward and no penalty parameters or additional degrees of freedom are used. The computational efficiency of the FS‐FEM is found better than that of the FEM. Copyright © 2008 John Wiley & Sons, Ltd.     

A contact analysis approach based on linear complementarity formulation using smoothed finite element methods

Based on the subdomain parametric variational principle (SPVP), a contact analysis approach is formulated in the incremental form for 2D solid mechanics problems discretized using only triangular elements. The present approach is implemented for the newly developed node-based smoothed finite element method (NS-FEM), the edge-based smoothed finite element method (ES-FEM) as well as standard FEM models. In the approach, the contact interface equations are discretized by contact point-pairs using a modified Coulomb frictional contact model. For strictly imposing the contact constraints, the global discretized system equations are transformed into a standard linear complementarity problem (LCP), which can be readily solved using the Lemke method. This approach can simulate different contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is conducted to investigate the effects of various parameters and validate the proposed method. The numerical results have demonstrated the validity and efficiency of the present contact analysis approach as well as the good performance of the ES-FEM method, which provides solutions of about 10 times better accuracy and higher convergence rate than the FEM and NS-FEM methods. The results also indicate that the NS-FEM provides upper-bound solutions in energy norm, relative to the fact that FEM provides lower-bound solutions.