水珠滴落的最小二乘粒子有限元方法模拟

提出了一种最小二乘粒子有限元方法,用其模拟了二维水珠滴落水面并飞溅散开的过程.该法基于拉格朗日描述,在每个时间步上使用扩展的Delaunay划分更新计算网格,并应用α形方法识别自由面形状;用最小二乘有限元方法离散流体运动的Navier-Stokes方程,并推导了一种自适应时间步长方案以提高计算效率和鲁棒性;引入网格拉伸技术修正减小流体质量误差.对水滴飞溅进行仿真,得到了与商用软件Flow-3d比较符合的结果,且具有更清晰锐利的自由面. 关键词： 滴落 网格划分 α形')" href="#">α形 最小二乘有限元     

比例边界有限元法在电机电磁场问题中的应用

将比例边界有限元法应用到电机磁场分析计算中,采用加权余量法推导无旋磁场的比例边界有限元方程及其离散格式,给出相邻子域公共边上内部节点磁位求解方法.以具有解析解的电机磁场问题为例进行计算和对比分析,验证离散格式的正确性和比例边界有限元法求解电机磁场的可行性,为该方法在电机磁场问题中的应用打下基础.     

空芯大气隙高温超导直线电机电磁力实验研究

直线电机是一种无需中间传动装置而直接将电磁力转换为线性运动的特种电机,在交通运输领域具有广泛的应用前景.将高温超导技术与电机理论相结合,能够有效利用超导材料的强载流能力与高场特性提高直线电机的输出能力.本文提出了一种应用于超导磁悬浮列车牵引的空芯高温超导直线电机,首先建立空芯高温超导直线电机的二维有限元模型对电机结构参数进行初步探索,并完成了超导直线电机样机的设计与制作.通过搭建实验测试平台完成了空芯高温超导直线电机定子磁场和电磁力的实验测试.有限元计算结果与实验数据有较好的一致性,验证了模型的有效性,并利用该模型研究了定子电流,超导线圈电流以及电机气隙对电机推进力输出的影响.本文的相关成果将促进超高速磁浮交通领域关键驱动技术的研究与发展.     

动磁式直线压缩机电磁特性分析及实验

设计开发了一种动磁式直线压缩机样机,利用磁路分析法对直线压缩机的静态特性进行定性分析,得到了电磁力、磁链关于电流、位移以及直线振荡电机结构参数之间的函数关系.又利用电磁场的二维有限元参数化分析进行定量分析,精确计算了不同位置和电流下的电磁力和磁链.修正了磁路分析的计算结果.为研究其动态特性,将有限元静态分析与状态方程法相结合,建立了动力学模型,并利用4阶Runge-Kutta法求解状态方程.实验证明,此动态特性仿真方法是有效的,样机的性能能够满足冰箱压缩机的前求.     

高温超导同步直线电机的数值仿真分析

利用Comsol Multiphysics多物理场耦合软件对单极高温超导直线电机进行有限元电磁仿真分析,首先详细介绍高温超导直线电机的二维仿真模型和计算流程,并通过计算结果和实验结果作对比的方法对该模型进行了有效性验证;利用仿真模型详细分析高温超导线圈几何参数对力学性能的影响:高温超导线圈匝数、高度对直线电机力学性能的影响;随着线圈匝数的增加,虽然最大推进力随匝数的增加而单调增加,但对应的作用力增量却随匝数的增加而逐渐减小.另外随着超导线圈高度的增加,当推进力达到一定饱和值后,继续增大线圈高度只能导致法向力的增大,却并不能带来推进力的进一步提高.最后重点讨论在高温超导带材线圈中引入铁磁材料后,铁芯和背部铁轭几何参数对直线电机作用力的影响.所得结论对高温超导直线电机的电磁结构设计具有指导意义.     

使用混合网格计算非达西渗流

针对垂直裂缝井的特殊流动模式,从非达西定律出发,建立二维平面的非达西渗流方程.通过建立一组无量纲量,最终得到无量纲的渗流方程及其定解条件.假定外边界为圆形,用PEBI网格及混合网格对求解区域进行网格划分,用有限差分法对无量纲的方程进行离散,最终得到垂直裂缝井的井底压力数值解.根据此数值解并考虑井筒存储和表皮因子的影响,得到真实垂直裂缝井的井底压力.对计算结果的分析表明,使用混合网格求解非达西渗流井底压力相当准确,该方法也适用于水平井等更复杂井型及复杂边界的问题求解.     

α铁冲击相变的离散元方法

利用离散元方法结合基于无扩散相变的两相模型、热力学相容的自由能函数与有限速率相变动力学方程,模拟α铁的冲击相变过程.得到铁的相边界、冲击Hugoniot关系及自由面速度剖面,并对不同冲击压力下加卸载过程的波系传播和相互作用过程进行分析,获得了加卸载波速特征.     

基于旋转场曲率的二维剪切梁单元建模

对二维剪切梁单元进行研究,利用平面旋转场理论推导了精确曲率模型.采用几何精确梁理论构建了剪切梁单元弹性力矩阵.通过绝对节点坐标方法建立了系统的非线性动力学方程,提出基于旋转场曲率的二维剪切梁单元,并分别引入经典二维剪切梁单元和基于位移场曲率的二维剪切梁单元进行比较研究.首先,静力学分析证明了所提模型的正确性;其次,特征频率分析验证了模型可与理论解符合,收敛精度高,并且能准确地预测单元固有频率对应的振型;最后,在非线性动力学问题上,通过与ANSYS结果对比分析,证明了该模型可有效处理柔性大变形问题,并且与经典二维剪切梁单元相比具有缓解剪切闭锁的优势.因此,本文提出的基于旋转场曲率的二维剪切梁单元在处理几何非线性问题中具有较大的应用潜力.     

解多种介质自由边界问题的边界元方法

本文讨论了非均匀介质自由边界问题的边界元解法,导出了具有弱奇性积分核的边界积分方程,并被用来处理分片均匀土坝的渗流自由面问题。     

典型自由面流动问题的SPH-ALE数值模拟

应用基于黎曼解的SPH-ALE方法对两种典型自由面流动问题进行数值模拟,并提出一种一阶核函数修正压力计算方法,通过对临近边界的水粒子压力进行核积分,近似估算固壁边界压力.给出不同时刻的流场压力分布及自由液面演化过程,将计算结果与相关的试验值及数值解进行对比,分析结果表明：SPH-ALE方法较传统SPH方法在流场压力计算精度上有较大的改进,在处理强非线性自由面流动问题时能够达到较高的精度.     

Calculation of transient dynamic stress intensity factors at bimaterial interface cracks using a SBFEM-based frequency-domain approach

A frequency-domain approach based on the semi-analytical scaled boundary finite element method (SBFEM) was developed to calculate dynamic stress intensity factors (DSIFs) at bimaterial interface cracks subjected to transient loading. Because the stress solutions of the SBFEM in the frequency domain are analytical in the radial direction, and the complex stress singularity at the bimaterial interface crack tip is explicitly represented in the stress solutions, the mixed-mode DSIFs were calculated directly by definition. The complex frequency-response functions of DSIFs were then used by the fast Fourier transform (FFT) and the inverse FFT to calculate time histories of DSIFs. A benchmark example was modelled. Good results were obtained by modelling the example with a small number of degrees of freedom due to the semi-analytical nature of the SBFEM. Supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China (Grant No. J20050924) and the Australian Research Council Discovery Project (Grant No. DP0452681)     

Modelling of water wave interaction with multiple cylinders of arbitrary shape

This paper describes the development of an efficient numerical model, namely scaled boundary finite-element method (SBFEM) for linear waves interaction with cylindrical structures of arbitrary shapes. The two-dimensional Helmholtz equation is firstly weakened in the circumferential direction, so that the governing partial differential equation is transformed to an ordinary matrix differential equation in radial direction, and is solved fully analytically. As a key element, a virtual porous circular cylinder surrounding the cylindrical structures is introduced so that the entire computational domain is partitioned along the virtual cylinder into an unbounded and several bounded sub-domains with common interfaces. The principle innovation is that, the present SBFEM model chooses Hankel function as a base solution for the unbounded sub-domain, while a power series is used for the internal bounded sub-domains. The approach discretises only the common interfaces of the sub-domains with surface finite-elements, and fewer elements are required to obtain very accurate results. Numerical simulations show that the new SBFEM model offers a considerable improvement by far in its numerical performance, as well as in the range of physical phenomena that is capable of simulating. The wave forces and run-ups are presented for a single and multiple cylindrical structures of different cross sectional shapes. Influences of the incident wave parameters and structural configurations on the hydrodynamics are examined.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

A clarification on the use of the Mellin transform in optical pattern recognition

The necessity of translating a scaled input function in the logarithmic coordinates necessary to perform an optical Mellin transform is demonstrated. The implications of this requirement in the processing of two dimensional inputs for pattern recognition are discussed.     

Generation of an elliptic Bessel beam

In an elliptic coordinate system the solution for a diffraction-free beam is given by a Mathieu beam, which is mathematically complicated and therefore takes considerable computational time and a large memory space. A technique is reported for the generation of elliptic hollow beams, which are actually scaled versions of higher-order Bessel beams. The analysis is based on the fact that stretching coordinates in the space domain results in a contraction of the coordinates in the frequency domain, along with a change in the overall amplitude of the spectrum. The beam, produced holographically, is structurally stable and retains its shape up to approximately 1 m.     

交会对接航天器间相对位姿参数单目视觉测量的解析算法

利用四个非共面设置的特征光标和单个CCD相机,采用单位四元素来描述航天器相对姿态,基于比例正交投影近似假设,建立目标航天器已知特征光标物理坐标和对应图像点图像坐标之间的简化数学模型,以解析的形式给出了航天器间相对位姿参数(相对位置和姿态),并对解析解进行修正。对该算法进行数学仿真,仿真结果表明,算法简单可靠,能够满足航天器确定精度和实时计算的要求。     

低渗透多孔介质非达西渗流动边界界面追踪

基于低渗透多孔介质非达西不稳定渗流的动边界数学模型,推导动边界移动速度的微分表达式,揭示动边界移动速度与动边界上地层压力关于径向距离的二次导数成正比;由此利用拉格朗日三点插值公式求得动边界附近控制方程的有限差分格式,并对下一时刻动边界的精确位置进行追踪.有限差分方法的数值结果表明界面追踪法可较好地反映低渗透多孔介质非达西不稳定渗流动边界的移动规律.     

A scaled boundary node method applied to two-dimensional crack problems

A boundary-type meshless method called the scaled boundary node method(SBNM) is developed to directly evaluate mixed mode stress intensity factors(SIFs) without extra post-processing.The SBNM combines the scaled boundary equations with the moving Kriging(MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter.As a result,the SBNM requires only a set of scattered nodes on the boundary,and the displacement field is approximated by using the MK interpolation technique,which possesses the δ function property.This makes the developed method efficient and straightforward in imposing the essential boundary conditions,and no special treatment techniques are required.Besides,the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction.Therefore,the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip.Numerical examples using the SBNM for computing the SIFs are presented.Good agreements with available results in the literature are obtained.