一种改进的分块隐式数值方法

提出了一种改进的分块隐式数值方法，在贴体坐标和交错网格下以逆变速度分量和压力Ｕ，Ｖ，Ｗ，ｐ为基本求解变量，由此克服了原分块隐式数值方法求解复杂边界流动时的困难．９０°弯管流动数值计算初步表明，本文提出的方法合理、可行     

磁流体力学数值计算处理方法

介绍电磁内爆实验中求解磁流体力学方程组的处理方法。方程组采用分裂法以克服非线性耦合可能引起的数值不稳定性；采用隐式差分格式避免过小时间步长限制。隐式格式采用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法叠代求解，使用比较简单的叠代初值的给定方法。对一些特殊边界处理作了说明。     

超高压环境下再生式喷雾燃烧过程的多维多相流数值模拟

液体药火炮内再生式喷雾燃烧过程的主要特点，一是处于超高压下，二是燃烧过程与决定液体喷射过程的移动边界高度耦合。建立了充分反映上述特点的多维多相流数学模型，对液滴相还考虑了液滴之间的碰撞与聚合以及液滴与湍流之间的相互作用。运用任意拉格朗日－欧拉数值方法进行了数值求解，得出了与实验基本一致的结果。给出并分析了过程各主要物理参量的时空分布，揭示了再生式喷雾燃烧过程的基本特征。     

统一格式的显式与隐式任意混合异步算法

动力学问题的有限元分析需要在每一时步求解系统信息,相对于静力学问题,其计算量要大得多.因而,提高计算效率,节省计算工作量是动力学求解方法研究的主要内容.该文针对大型复杂动力学系统的高效求解问题,提出了一种基于Newmark离散格式的显式、隐式任意混合异步算法,根据整体系统不同局部的物理力学特性和求解精度要求,在空间域及时间域内对动力学系统方程进行多尺度求解.该方法根据显式、隐式算法固有的信息传递机制,采取动态的可变边界处理方法,避免了异步边界上的误差积累;并通过对整体系统能量平衡的校验,动态地确定和修正仿真计算时步,可以有效地预防不稳定性的产生和发展.数值算例表明:该算法能在保持较高的计算精度的同时,极大地降低计算资源消耗,因而具有一定的实用价值.      

分块隐式有限差分法计算弯管紊流

本文利用贴体坐标系中分块隐式有限差分法计算矩形截面90°弯管中不可压恒定紊流.在计算中,雷诺方程的数值离散采用混合差分格式,局部联立求解雷诺方程和连续方程而得到速度压力解.在全流场的迭求解过程中采用对称联立Gauss—Seidel法.利用标准K-ε紊流模型模拟紊流.计算结果与有关试验进行了对比.     

自由边界载流等离子体柱的电阻螺旋模不稳定性的数值分析

本文导出了自由边界载流等离子体柱的电阻螺旋模所满足的方程和定解条件,采用了对时间步长的两步隐式差分法进行数值求解。发现,温度剖面的加宽和增大,对等离子体起显著的增稳作用。     

隐式重启动Arnoldi/Lanczos法的子区域并行算法

针对求解有限元分析的特征值问题,提出了一种隐式重启动Arnoldi/Lanczos方法的子区域并行算法。隐式重启动Arnoldi/Lanczos利用重启动技术以提高所需谱的收敛性,并能有效处理Krylov基形成问题、存储所需的内存问题、计算成本问题。并行算法中采取子区域接子区域方法、重叠和非重叠网格划分技术。采用压缩数据结构来储存系数矩阵。对Krylov的数值线性代数运算和隐式重启动法中的数值线性代数运算的并行化进行了研究。数值算例表明:该算法具有良好的适用性和效率,适合分布式储存体系的机群。     

弹塑性问题参数二次规划分析的隐式算法

传统的二次规划算法求解弹塑性问题时一般要经过对问题的线性化,如对屈服条件的一阶近似展开等,这在一定程度上会造成数值解的误差。为此,本文提出一种改进的策略,引入迭代与规划算法相结合的技术对问题进行处理,算法收敛平稳迅速,在大步长荷载增量下使算法的精度大大提高。由于本文的算法属于隐式算法,因而也就弥补了原二次规划算法求解弹塑性问题时只有显式算法的不足,从而达到了对原算法的进一步完善。     

基于PANDA的并行显式有限元程序开发

冲击响应数值模拟在军用与民用领域有广泛的应用需求,但现有串行分析程序难以满足求解规模和效率的需求,因此需要开发并行显式有限元程序.本文在分析了显式有限元串行基本算法的基础上,设计了相应的并行算法,采用模块化程序开发模式基于PANDA程序框架开发了并行显式有限元分析程序DynPack,并进行了算例验证.算例表明,DynP...     

基于神经网络的隐式显化方法在结构可靠度分析中的应用

针对结构可靠度分析中极限状态方程不能明确表达的情况,结合神经网络技术,提出了隐式极限状态方程转换为显式表达式的方法.该方法利用神经网络的非线性映射能力,构造出显式表达的极限状态方程,从而可以很方便的引入一次二阶矩等其他基本求解方法进行结构可靠度分析.实例数值结果表明,基于神经网络将隐式函数转化为明确表达的极限状态方程是可行的,同时该方法具有较高的精度,为结构可靠度计算提供了新的有效思路和手段.     

加权残数法通用程序包MWRAP的开发技术与1程应用

要想使加权残数法广泛应用于工程实际问题,需要解决两方面的问题,一是精度问题,二是必须研制和开发通用软件。本文阐述了加权残数法通用程序包MWRAP的结构设计和功能设置及其前后处理技术,详细阐述了其前后处理程序的程序设计流程;在该软件中计算模块,所用的计算方法为加权残数和有限元耦合法,为此推导了加权残数和有限元耦合法的公式,从计算结果来看该方法具有较高的精度,可以满足工程需要。最后,运用MWRAP计算了钢管混凝土柱肩梁结构的位移和应力,与实验结果相比吻合较好,说明了MWRAP具有较高的精度,加上其完善的前后处理功能,可以应用于工程实际问题。     

计算含动边界非定常流动的无网格算法

在无网格算法中考虑了含动边界的流动问题,研究了可以计算处理包含一定位移及扭转动边界非定常流动的算法.创建了无网格算法的动点法则,并引入抗扭方法对弹簧方法进行改进来处理离散点运动,提高了方法的可用度及精度.发展了求解基于无网格的ALE方程组的算法,在点云离散的基础上采用曲面逼近计算空间导数及HLLC格式计算数值通量,运用四步龙格-库塔法进行时间推进.在跨、超音速条件下,计算模拟了典型翼型简谐振动流场,计算结果与实验结果及文献对比吻合,验证了该算法的正确性.     

A novel method for residual strength prediction for sheets with multiple site damage: Methodology and experimental validation

A unified method for solving the strip yield model for collinear cracks in finite and infinite sheet is proposed. The method is based on the weight function of a single crack. Two collinear cracks in finite and infinite sheets are used to apply and verify this method. The plastic zone size, crack opening displacement and stress distribution along the ligament between cracks obtained by using the present method are extensively compared with existing available results and finite element solutions, and very good agreements are observed. Combined with the Crack Tip Opening Angle (CTOA) criterion, the unified method is used to predict the crack growth behavior and residual strength for 2024-T3 aluminum alloy sheet with Multiple Site Damage (MSD). Thirty-two sheets with four types of MSD are designed and tested to verify this method. It is shown that the present method is able to predict various crack growth behaviors observed in experiment. The predicted residual strengths are within 9% of the corresponding test results. Compared to the elastic–plastic finite element method, the present method is much more efficient.     

带源参数的二维热传导反问题的无网格方法

利用无网格有限点法求解带源参数的二维热传导反问题，推导了相应的离散方程. 与 其它基于网格的方法相比，有限点法采用移动最小二乘法构造形函数，只需要节点信息，不 需要划分网格，用配点法离散控制方程，可以直接施加边界条件，不需要在区域内部求积分. 用有限点法求解二维热传导反问题具有数值实现简单、计算量小、可以任意布置节点等优点. 最后通过算例验证了该方法的有效性.     

High-order methods for differential equations with large first-derivative terms

A method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non-linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one-dimensional case an approximating equation is developed using just three points. The method first presented is a fourth-order approximation but is extended to become a higher-order method. Results are included for the fourth-, sixth-, eighth- and tenth-order methods. The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie. The method of this paper was also tested on the solution of some non-linear diffusion equations with concentration-dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two-dimensional problems. The method developed in this paper is accurate, easy to use and can be generalized to other problems.     

Collocated discrete least squares meshless (CDLSM) method for the solution of transient and steady‐state hyperbolic problems

A collocated discrete least squares meshless method for the solution of the transient and steady‐state hyperbolic problems is presented in this paper. The method is based on minimizing the sum of the squared residuals of the governing differential equation at some points chosen in the problem domain as collocation points. The collocation points are generally different from nodal points, which are used to discretize the problem domain. A moving least squares method is employed to construct the shape functions at nodal points. The coefficient matrix is symmetric and positive definite even for non‐symmetric hyperbolic differential equations and can be solved efficiently with iterative methods. The proposed method is a truly meshless method and does not require numerical integration. Advantages of the collocation points are shown to be threefold: First, the collocation points are shown to be responsible for stabilizing the method in particular when problems with shocked solution are attempted. Second, the collocation points are also shown to improve the accuracy of the solution even for problems with smooth solutions. Third, the collocation points are shown to contribute to the efficiency of the method when solving steady‐state problems via faster convergence of the resulting algorithm. The ability of the method and in particular the effect of collocation points are tested against a series of one‐dimensional transient and steady‐state benchmark examples from the literature and the results are presented. A sensitivity analysis is also carried out to investigate the effect of the base polynomials on the accuracy and convergence characteristics of the method in solving steady‐state problems. The results show the ability of the proposed method to accurately solve difficult hyperbolic problems considered. The method is also shown to be particularly stable for problems with shocked solution due to the inherent stabilizing mechanism of the method. Copyright © 2008 John Wiley & Sons, Ltd.     

一种空间缆索结构静力分析的解析元法

将空间缆索结构简化为具有拉伸刚度的质点系,给出了缆索结构空间解析元法的基本方程和求解方法,单元间的作用力与坐标变化的关系可以用解析法得到,对所得到的反映结构特性的质点系方程组进行力的平衡迭代,求解方程组.采用自动的动态可变步长的迭代方法,能够提高计算效率,保证收敛.这种方法既考虑了几何非线性,又适用于材料非线性的计算,比有限元法优越之处还在于,它不用求解线性方程组,所以适用范围广,允许求解多自由度的几何可变体系,而有限元法在求解此类问题时经常不收敛.     

基于Steffens-Newton法的空间索形悬索桥初始平衡状态分析

空间索形悬索桥的主缆、吊索相互耦合,用数值解析法精确求解其初始平衡状态时,面临收敛困难、算法要求严格的问题。本文建立了空间缆索的平衡方程,推导了误差调整方程。分别证明了平面索形所常用的线形变化刚度法及影响矩阵法在空间索形中不再适用。基于可调参数的Steffens-Newton法,提出一种高效的空间缆索耦合体系分析方法,...     

非定常流函数涡量方程的一种数值解法的研究

对非定常流函数涡量方程的数值求解方法进行了改进,其中流函数一阶导数即速度项采用四阶精度的Hermitian公式,对流项由一般二阶精度的中心差分提高到四阶精度离散差分,包含温度方程在内的离散方程组采用ADI迭代方法求得定常解．以无内热体及有一内热体的封闭方腔内自然对流为例,进行了不同瑞利数（Ra）条件下的数值研究．结果表明,该方法推导简单,求解精度高且计算稳定,适用于封闭腔内高瑞利数复杂混合对流的数值模拟．     

一种从离散模拟到连续介质弹性模拟的过渡方法

提出了一种从离散分子动力学模拟(MD)到连续介质弹性有限元计算分析(FEA)的过渡方法, 简称MD-FEA方法. 首先通过MD计算获得晶体材料原子的移动位置, 然后根据晶体结构的周期性特征构造连续介质假设下的有限单元变形模型, 进一步结合材料的力学行为本构关系获得应变和应力场. 为了检验MD-FEA方法的有效性, 将该方法应用于详细分析Al-Ni软硬组合两相材料纳米柱体的拉伸变形问题和基底材料为Al球形压头材料为金刚石的纳米压痕问题. 采用MD-FEA方法获得了上述两种问题的应力?应变场, 并将计算结果分别与传统MD方法中通过变形梯度计算的原子应变以及原子的位力应力进行了比较, 详细讨论了用MD-FEA方法计算的应力?应变场与传统MD原子应变和位力应力的区别, 并对MD-FEA方法的有效性及其相较于传统MD方法所具有的优势进行了探讨. 结论显示, MD-FEA方法与传统MD方法在应力?应变变化平缓的区域得到的结果接近, 但在变化剧烈的区域以及材料的表/界面区域, MD-FEA方法能够得到更加精确的结果. 同时, MD-FEA方法避免了传统MD方法中, 需要人为选取截断半径以及加权函数所导致的误差. 另外, 当应变较大时, MD-FEA方法计算的小应变与传统MD方法计算的格林应变存在一定差异, 因此, MD-FEA方法更适合应变较小的情形.