多元件谐振腔模式的有限元传输矩阵分析方法

建立了多元件谐振腔本征模的有限元传输矩阵模型。提出了模式计算相对误差概念及相应表达式,该表达式在数值上不受菲涅耳数的影响,能够很好反映有限单元划分方案对不同菲涅耳数的谐振腔的模式计算精度的影响。提出了有限单元划分精细度的概念和相应表达式,用以表征有限单元划分的精细程度。该表达式以菲涅耳数作为有限元传输矩阵法对腔镜单元格数划分的相对要求,用镜面实际划分的单元格数与菲涅耳数的比值来表征有限单元划分的精细程度。分析了不同谐振腔参数变化时模式计算相对误差与有限单元划分精细度的关系,建立了3种不同函数形式的经验表达式,并通过比较拟合残差选择了拟合效果较好的表达式。     

一种抗单元逆转的软组织有限元模型

由于Green应变具有单元翻转不变性,在大变形的仿真中有可能会出现单元的逆转,破坏模型网格的拓扑结构,导致仿真失败,因此提出一个新的有限单元模型,在采用Green应变度量变形同时把单元体积变化率和单元内压强关系引入到本构方程中,解决单元逆转问题;同时,模型导出的单元弹性势能是单元结点位移的多项式函数,有效地简化了共轭梯度法的求解,效率显著提高.实验结果表明,该模型可以应用于软组织大变形的实时仿真中.     

金属一氧化物一半导体电子存贮器

比较了不同类型半导体存贮单元的选取时间、存贮性、容量及成本。也比较和估算了半导体存贮系统、铁氧体系统及磁致伸缩延迟线系统。     

在曲线坐标系中流线曲率法与有限差分法的比较

大功率透平机械叶栅流道的边界是相当复杂的.当采用圆柱坐标系时,对矩阵法和流线曲率法,需要单独处理流道边界上“破碎”的网格,这无疑增加了计算时间;如不处理则会降低计算精度.采用有限元素法虽然可以避免单独处理边界上的计算网格,但计算时间长和需要存贮单元多则是它的最大缺点.我们采用的在曲线坐标系中的流线曲率法和矩阵法既不必单独处理边界上的计算网格,也不要很多的存贮单元和过长的计算时间. 目前已发表的文章几乎都未涉及到将计算站设立在叶片流道内时,流线曲率法和矩     

用单块电子俘获器件实现可编程二值光学逻辑处理

用单块电子俘获器件,以一种新方法一时域编码方法,实现了所有16种布尔逻辑运算.根据电子俘获材料的存贮和可擦除特性,按特定顺序进行一系列单元操作,可测到每种布尔逻辑函数,同一般光学逻辑处理器相比,这种处理器具有新的自由度一时域自由度,文末给出了实验结果.     

基于光线追踪的实时可交互计算生成集成成像方法

为提高计算生成集成成像实时交互显示性能和灵活性,构建与集成成像再现系统结构一致的集成光场视见模型,通过该模型为单元图像阵列中每个像素生成一条逆向追踪的光线,使用光线追踪技术并行渲染光线为单元图像阵列像素着色.实验结果表明,顶点数为565 880的点云模型、面数为977 308的含纹理网格模型在透镜数为22×13、视点数为175×175的4K显示系统上显示帧率40fps以上,并实现了缩放、移动、旋转、显示微调等交互功能.该方法摆脱了虚拟相机模型,降低了算法复杂度,利于实现实时交互,能够应用于基于不同分布形式透镜阵列的集成成像显示系统.     

六面体单元上的控制体有限元方法

针对四面体单元在三维几何域的网格剖分中单元数过大，导致计算中过多占用机时与内存的问题，建立了六面体单元上的控制体有限元方法，采用散度定理将对结点所建立在控制体上的体积分转化为在相应控制面上的面积分，使之对对流项变量可采用迎风插值格式，通过算例表明，在受计算机内存及速度的限制下，该方法可作为三维流动与传热问题数值模拟的一种有效方法。     

一种改进型HOPFIELD神经网络模型及其单通道光学实现

提出一种改进型HOPFIELD神经网络模型。通过对存贮模式进行互补扩展,消除了存贮模式中0和1个数不等问题。利用扩展模式互补性和由扩展模式所形成的连接权的镜象对称性,在不增加神经元个数和连接权矩阵维数的情况下,提高了网络的存贮能力和容错能力。在此基础上设计了全正光学连接权矩阵,在单通道内实现了双极寻址,降低了光学系统的复杂性。     

换热器的效能与熵产分析

本文给出了以进口冷热流体温度、热容量流比和传热单元数表示的顺流、逆流及两边混合的叉流换热器熵产数的分析表达式，研究了这三类换热器熵产数随热容量流比及传热单元数变化的规律，给出了由于不平衡流动和传热面积有限产生的熵产数的表达式。分析表明，在进、出口温度均匀条件下换热器效能与熵产数之间存在一一对应的关系，效能与熵产数一样，所表征的是换热器热力学第二定律的完善程度。     

基于电力电子低温应用的超导电力集成研究

本文探讨了基于电力电子低温应用的超导电力集成的基本概念,分析了集成设计的基本原理.提出了超导集成低温功率系统应用的三种基础单元:超导集成低温DC/DC单元、超导集成低温AC/DC单元以及超导集成低温整流桥单元.它们将电力电子低温应用与超导电力应用有机的集成了起来,实现了无引线磁体功率系统、电压补偿型超导限流器以及无需偏压源的超导限流器等新的超导电力应用.最后讨论了实现超导集成低温功率系统的关键技术.     

磁性液体材料微结构磁化状态数值分析

采用磁性液体边界元数值模型分析了磁性粒子微结构磁化状态及相互作用,并与相应的有限元数值结果进行比较．结果表明：虽然粒子边界层附近的磁场分布出现了一定的模糊,且变化幅度明显高于有限元结果,但在粒子边界层以外的其它区域两种数值解法具有高度一致性;当粒子边界元节点数较小时,磁力相互作用边界元结果与有限元结果相差较大,且很不稳定;随着节点数增加,边界元结果逐渐趋近于有限元虚功原理的磁力数值结果,并达到一个较稳定的量值．结果清晰地反映出边界元数值方法在磁性液体多体动力学模拟研究中的一些基本特征。     

Improved eigenvalues for combined dynamical systems using a modified finite element discretization scheme

New approaches are presented to discretize an arbitrarily supported linear structure carrying various lumped attachments. Specifically, the exact eigendata, i.e., the exact natural frequencies and mode shapes, of the linear structure without the lumped attachments are first used to modify its finite element mass and stiffness matrix so that the eigensolutions of the discretized system coincide with the exact modes of vibration. This is achieved by identifying a set of minimum changes in the finite element system matrices and enforcing certain constraint conditions. Once the updated matrices for the linear structure are found, the finite element assembling technique is then used to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices. Numerical experiments show that for the same number of elements, the proposed scheme returns higher natural frequencies that are substantially more accurate than those given by the finite element model. Alternatively, the proposed discretization scheme allows one to efficiently and accurately determine the higher natural frequencies of a combined system without increasing the number of elements in the finite element model.     

A hexahedron element formulation with a new multi-resolution analysis

A multiresolution hexahedron element is presented with a new multiresolution analysis(MRA)framework.The MRA framework is formulated out of a mutually nesting displacement subspace sequence,whose basis functions are constructed of scaling and shifting on element domain of a basic node shape function.The basic node shape function is constructed from shifting to other seven quadrants around a specific node of a basic isoparametric element in one quadrant and joining the corresponding node shape functions of eight elements at the specific node.The MRA endows the proposed element with the resolution level(RL)to adjust structural analysis accuracy.As a result,the traditional 8-node hexahedron element is a monoresolution one and also a special case of the proposed element.The meshing for the monoresolution finite element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the solid mathematical basis.The simplicity and clarity of shape function construction with the Kronecker delta property and the rational MRA enable the proposed element method to be more rational,easier and efficient in its implementation than the conventional mono-resolution solid element method or other MRA methods.The multiresolution hexahedron element method is more adapted to dealing with the accurate computation of structural problems.     

A general finite element model for numerical simulation of structure dynamics

A finite element model used to simulate the dynamics with continuum and discontinuum is presented. This new approach is conducted by constructing the general contact model. The conventional discrete element is treated as a standard finite element with one node in this new method. The one-node element has the same features as other finite elements, such as element stress and strain. Thus, a general finite element model that is consistent with the existed finite element model is set up. This new model is simple in mathematical concept and is straightforward to be combined into the existing standard finite element code. Numerical example demonstrates that this new approach is more effective to perform the dynamic process analysis in which the interactions among a large number of discrete bodies and continuum objects are included.     

考虑通孔和边缘效应的互连网络热电分析

考虑互连通孔和边缘效应,建立互连层间、层内、通孔热阻模型,利用热电二元性,提出一种考虑温度效应对热流影响的热电耦合仿真方法,利用热电之间的反馈关系,修正建模后的温度分布对节点网络热流的影响.并对以聚合物和硅氧化物为介质的多层互连进行分析,以有限元建模结果为参照,与已有模型相比,互连热分布结果的相对标准差分别降低了71.2%、12.9%.考虑通孔效应和边缘效应后,该方法在不同纳米级工艺中所得峰值温升,较已有模型均有一定程度的降低.     

弯张换能器装配预应力及入水后的变化

精确控制施加于驱动元件上的预应力，对换能器的设计及其工作过程都有重要意义，特别对于稀土磁致伸缩换能器来说，有助于发挥其最大潜能.利用有限元方法，计算了VII型水声弯张换能器壳体给驱动元件施加一定预应力时，壳体所需的装配位移的大小，并通过实验作了验证；弯张换能器随入水深度的不同， 驱动元件两端所受到的总的预应力是不同的.利用有限元方法，计算了换能器入水深度与预应力的关系.本文方法可适合于其他任何类型的换能器. 关键词： 弯张换能器 装配位移 预应力 入水深度     

多孔介质两相流的局部守恒有限元分析

用局部守恒有限元法研究多孔介质两相渗流问题.详细阐述局部守恒有限元法的基本原理,推导两相渗流问题的局部守恒有限元计算格式并编制相应的计算程序.通过一维Buckley-Leverett两相渗流算例验证该方法的正确性.应用局部守恒有限元法和混合有限元法分别对2个模型进行分析对比.计算结果表明局部守恒有限元法具有良好的鲁棒性及适用性,相较于混合有限元法,处理过程简单,计算时间缩短,为标准有限元法应用于复杂渗流问题提供了一种途径.     

OPTIMIZATION OF SIMPLIFIED MODELS MESHED WITH FINITE TRIANGULAR PLATE ELEMENTS

Designers often want to analyze more and more sophisticated structures, thus leading to very large finite element models (typically 10 00 000 degrees of freedom for a body car, for example). These models being too costly for the early stages of design and optimization can be reduced by a substructure analysis or a mesh simplification of the components. A methodology is proposed in this paper for simplifying finite triangular plate element models leading to a dramatic reduction in the number of degrees of freedom while preserving the dynamical properties of the initial system. In particular, the proposed method is developed for models composed of the plate element STIFF63 generated by the software ANSYS. The principle consists in determining the parameters (thickness, Young's modulus, density) of the triangular elements of a coarse model which replaces a large set of elements of the refined model. The simplified mesh must satisfy one of two criteria. The first requires that the mass and stiffness matrices of the simplified model be as close as possible to the Guyan condensed matrices of the refined model on the reduced node set, whilst the second requires that the dynamical properties of the global structure be preserved. The application of these approaches is illustrated on two test structures using the gradient method to solve the resulting optimization problem. The second approach is shown to give the best results. Typically, the size of the models can be reduced by a factor of 20 whilst preserving the dynamical properties of the structure at low frequencies.     

Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems

A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh resolution down to the finest scales and multiscale methods capable of capturing the large scale components of the solution on macroscopic meshes are needed. Recently, the finite element heterogeneous multiscale method (FE-HMM) has been proposed for such problems, based on a macroscopic solver with effective data recovered from the solution of micro problems on sampling domains at quadrature points of a macroscopic mesh. Departing from the approach used in the FE-HMM, we show that interpolation techniques based on the reduced basis methodology (an offline-online strategy) allow one to design an efficient numerical method relying only on a small number of accurately computed micro solutions. This new method, called the reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is significantly more efficient than the FE-HMM for high order macroscopic discretizations and for three-dimensional problems, when the repeated computation of micro problems over the whole computational domain is expensive. A priori error estimates of the RB-FE-HMM are derived. Numerical computations for two and three dimensional problems illustrate the applicability and efficiency of the numerical method.     

基于改进格林元的压裂水平井动态分析方法

以建立高效的动态分析方法为出发点,以边单元作为求解点,改进传统的格林元方法,减少未知数和求解矩阵维度;并提出基于改进格林元的加密网格加密方法,保证考虑复杂裂缝网络的压裂水平井动态模拟的早期精度.退化模型与半解析解、数值模拟结果进行对比,验证本文基于加密网格的改进格林元方法的准确性和动态分析的高效性.最后进行动态响应的敏感性分析,结果表明：①格林元方法是一种高精度的动态模拟方法,将求解节点设置在网格的边上可以提高压裂水平井动态模拟的速度;②改进格林元方法的加密基于叠加原理,不需要通过插值近似,其求解精度高.在相同加密网格条件下,基于本文改进格林元方法的加密效果比有限差分加密效果更佳;③复杂裂缝导流能力、改造区渗透率提高倍数、改造区大小等参数对压裂水平井动态特征影响较大,在动态分析和参数反演时,应着重考虑这些因素的影响.