时-空混和元与多辛

指出所谓多辛相当于时间-空间混和坐标内的分别离散的规则网格;而时-空混和元则不用对时间、空间分别离散,而是组成混和的时空混和有限元网格,更加灵活些。     

车-桥系统耦合振动响应的简便计算

依据振动理论推导出了二自由度模型车辆与桥梁系统竖向耦合振动微分方程，采用模态分析的离散化方法，将复杂的偏微分方程问题转化为变系数常微分方程问题，并将微分方程数值积分的Runge-Kutta方法引入到该时变系统的振动响应计算中，使复杂的耦合响应问题得到简便的解决。通过算例验证了该方法的有效性和简便性。该方法只需要直接数值积分，具有公式简单，编程方便，计算速度快等优点，特别适合于工程实际问题的计算，并且不仅适用于匀速运动车辆，也适用于变速运动车辆。     

求解定常势流正命题的全时-空变分有限元法

非定常流动变分原理的建立使得用有限元法来求解多工况点的设计问题成为可能。本文在刘高联的非定常变分理论的基础上，对定常变分问题进行时间相关有限元求解。但由于可压缩非定常位势流动的控制方程是双曲型的，简单地把时间当作同空间一样的物理维来求解是不可行的。而现有的时-空有限元法极其复杂，增加了计算复杂度，使其很难用于工程设计中。为此，文[2、3]提出了求解一维非定常问题的新型时-空有限元法。本文把该方法推广到二维流动，用它求解二维弯管内的流动和翼型绕流问题。计算结果与用定常方法求得的结果几乎重合，说明该方法可以用于多维时间相关求解。     

锁骨三维有限元应力分析

根据CT扫描数据,运用Mimics软件建立肩胛骨和锁骨三维模型,导入Ansys软件并添加CT扫描数据无法识别的韧带,最后建立完整的肩锁关节三维有限元模型。根据肩部关节的协调运动确定边界条件,并施加载荷,计算得出盂肱关节外展30°、60°、90°及120°工况下肩锁关节应力分布。结合脆性材料破坏形式与应力状态的关系,可以判别锁骨骨折及骨裂的易发部位。结果表明:锁骨上表面中1/3靠近远端处Mises等效应力及最大主应力均较大,此处最大主应力为拉应力,易出现骨断裂即骨折;锁骨下表面中1/3靠近近端处Mises等效应力较大,此处最大主应力为压应力,易出现骨碎裂即骨裂。     

基于联合有限元-离散元的混凝土重力坝破坏三维仿真模拟

水利工程中混凝土重力坝在地震等作用下的三维破坏形式以及破坏过程对大坝安全影响重大。本文建立了固体材料的联合有限元-离散元(Combined Finite-Discrete Element)三维数学模型,并引入Single/Smeared断裂损伤模型,模拟混凝土材料的破坏。数学模型经验证后,用于地震作用下混凝土重力坝破坏的三维数值模拟,结果表明,联合有限元-离散元方法能够有效模拟坝体的破坏模式和破坏阈值条件,且具有将坝体连续变形与不连续断裂有机结合的优点。通过一系列数值模拟工况的对比,分析了模型网格分辨率对破坏条件、破坏模式以及程序计算效率的影响,研究结果能够为大坝的抗震设计提供有价值的参考。     

小波插值方法自适应数值求解时间进化微分方程

应用小波自相关函数的插值性质,得到任意给定函数的插值小波表达式,然后对其直接求导,可以得到函数导数的表达式。导数运算不再应用差分算法,扩展了小波方法在数值求解微分方程中的应用。由于小波基函数的有限支撑特点,小波方法可以有效地处理微分方程中解的局部突变问题。通过设定小波系数阀值,实现了求解过程的自适应。本文给出了两个算例,结果表明了算法的自适应特点及其向二维空间问题推广的有效性。     

考虑膨胀力的非饱和介质热-水-应力耦合二维有限元分析

从建立应力平衡方程、水连续性方程、能量守恒方程和弹塑性矩阵入手,使用Galerkin方法,将各控制方程分别在空间域和时间域进行离散,开发出了一个可考虑膨胀力的用于分析非饱和介质中热-水-应力耦合弹塑性问题的二维有限元程序.通过对一个假定的核废料地下处置库的热-水-应力耦合问题的数值计算,比较了无、有膨胀力时的情况,在定性上验证了该程序的正确性.     

含缺口复合材料层合板的三维有限元失效分析

本文研究了复合材料层合板最终强度计算的有限元理论,讨论了修正的Newton-Raphson迭代方法在层合板失效过程中应力场计算的迭代过程.同时本文建立了带缺口的复合材料层合板三维有限元模型,充分考虑层合板的纤维断裂、基体开裂和分层三种失效模式,采用修正的三维Hashin准则作为失效判断的依据,计算了三种不同铺层的层合板最终失效载荷值,与试验值吻合得很好.鉴于层压板材料常数ν23的数值难于测定的特点,讨论其对最终失效载荷的影响.在三维有限元模型的基础上,实现了失效扩展仿真分析.     

考虑土-结构相互作用效应的三维桩基结构动力有限元分析

结合简化阻抗法建立了三维相互作用结构的动力有限元分析模型,导出了考虑群桩刚体、惯性效应作用时的结构相互作用时程积分方程式,以近乎纯结构有限元的建模途径合理地反映出桩-土-上部结构在水平地震作用下的动力相互作用特性。模型中引入具有桩(筏)-土阻抗特性的弹阻单元来描述不同群桩布置、土层状况因素对体系反应的参与作用,而在动力方程中竖向SV剪切波经桩土刚体相互作用产生的水平、摇摆分量对体系的影响亦得以体现。20层桩承刚框架结构的动力分析表明:较柔的桩、土基础使得体系的SSI效应增强,但其参与程度与群桩效应相关,而结构构件内力较不考虑相互作用时有较大折减;应用该法可精确、快速地进行复杂上、下部结构时程反应分析。     

有限元-康托洛维奇杂交法及其应用

本文将有限元法与康托洛维奇方法进行适当组合,吸收二者的主要优点,提出在单元的位移插值函数中附加康托洛维奇项。康托洛维奇方法是一种半解析法,其在解析方向具有较高的精度,在一定程度上弥补了原有限元方法中插值函数选取的盲目性,能够较好地反映微分方程的固有性质,提高其适应性。在单元的位移插值函数中附加内部无节点的位移项,无需增加新的单元与节点,使用较少的单元即可获得较高的精度。并且,这些附加项满足单元边界条件为零,故其在单元与单元的交界面上是保证协调的。本文通过算例充分说明了此方法的特点和优越性。     

A moving finite element method for the population balance equation

A moving finite element algorithm has been compared against the upwind-differencing and Smolarkiewicz methods for the population balance equation of multicomponent particle growth processes. Analytical solutions and an error function have been used to test the numerical methods. The moving finite elements technique is much more accurate than other methods for a wide range of parameters. Since this method uses moving grids, it is able to model very narrow particle size distributions. It is also shown that the method can be extended to solve condensational growth problems which include particle curvature and non-continuum mass transfer effects.     

区段混合能的偏微分方程

结构力学与最优控制模拟关系的共同基础就是分析力学,表明在结构力学与最优控制理论的架构内也应有分析力学的整套理论。传统分析力学总是考虑连续时间、同时的状态、不变维数的体系。并且物性为即时响应的。但结构力学有限元要考虑离散坐标、不同坐标状态、而且变动维数、时滞的体系。根据区段变形能只与其两端位移有关,就可通过数学分析得到Lagrange括号与Poisson括号等内容。区段变形能就是作用量,满足Hamilton-Jacobi方程。但还有区段混合能的表示,本文证明它满足雷同的偏微分方程。它们在离散体系时还有偏差分方程。本文进一步给出了其与Riccati方程的关系。     

Criteria for finite element algorithm of generalized heat conduction equation

To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized heat conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.     

结构阻尼时域本构模型及其应用

阻尼合金作为一种新型结构功能材料在不少领域已获应用,由于其阻尼值较大且随频率呈复杂交化关系,传统的线性粘性阻尼理论或经典的非频变结构阻尼理论难以精确地描述其耗能行为。本文应用粘弹性阻尼理论,根据阻尼合金储能模量和损耗因子在频域的实测数据．应用最优化方法拟合出标准线性体模型中的本构参数;根据积分形式的三参量本构关系和变形体虚功原理,推导出了有限元形式的动力学方程;讨论了三参数初值的选取;对包含卷积积分的有限元动力学方程通过数学推导将其化为三阶线性微分方程组,再转化为标准状态变量方程,应用数值求解。数值计算实例证明了所提方法的正确和有效性。     

White in Time Scalar Advection Model as a Tool for Solving Joint Composition PDF Equations

A rapidly decorrelating velocity field model is used to derive stochastic partial differential equations (SPDE) allowing one to compute the modeled one-point joint probability density function of turbulent reactive scalars. Those SPDEs are shown to be hyperbolic advection/reaction equations. They are dealt with in a generalized sense, so that discontinuities in the scalar fields can be treated. The Eulerian Monte Carlo (EMC) method thus defined is coupled with a RANS solver and applied to the computation of a turbulent premixed methane flame over a backward facing step.     

Particle trajectory calculations with a two‐step three‐time level semi‐Lagrangian scheme well suited for curved flows

This study proposes a new two‐step three‐time level semi‐Lagrangian scheme for calculation of particle trajectories. The scheme is intended to yield accurate determination of the particle departure position, particularly in the presence of significant flow curvature. Experiments were performed both for linear and non‐linear idealized advection problems, with different flow curvatures. Results for simulations with the proposed scheme, and with three other semi‐Lagrangian schemes, and with an Eulerian method are presented. In the linear advection problem the two‐step three‐time level scheme produced smaller root mean square errors and more accurate replication of the angular displacement of a Gaussian hill than the other schemes. In the non‐linear advection experiments the proposed scheme produced, in general, equal or better conservation of domain‐averaged quantities than the other semi‐Lagrangian schemes, especially at large Courant numbers. In idealized frontogenesis simulations the scheme performed equally or better than the other schemes in the representation of sharp gradients in a scalar field. The two‐step three‐time level scheme has some computational overhead as compared with the other three semi‐Lagrangian schemes. Nevertheless, the additional computational effort was shown to be worthwhile, due to the accuracy obtained by the scheme in the experiments with large time steps. The most remarkable feature of the scheme is its robustness, since it performs well both for small and large Courant numbers, in the presence of weak as well strong flow curvatures. Copyright © 2009 John Wiley & Sons, Ltd.     

High accuracy time and space transform method for advection–diffusion equation in an unbounded domain

A new numerical method called high accuracy time and space transform method (TSTM) is introduced to solve the advection–diffusion equation in an unbounded domain. By a spatial transform, the advection–diffusion equation in the unbounded domain Rⁿ is converted to one on the bounded domain [?1, 1]ⁿ, and the Laplace transform is applied to eliminate time dependency. The consequent boundary value problem is solved by collocation on Chebyshev points. To face the well‐known computational challenge represented by the numerical inversion of the Laplace transform, Talbot's method is applied, consisting of numerically integrating the Bromwich integral on a special contour by means of trapezoidal or midpoint rules. Numerical experiments illustrate that TSTM has exponential rate in time and space. Copyright © 2008 John Wiley & Sons, Ltd.     

精细时程积分法及其数值衍生格式应用评估

旋翼气动弹性耦合动力学方程本质上是一组刚性比较大的非线性偏微分方程。在有限元结构离散后,可改写为非齐次微分方程组,其中非齐次项是桨叶运动量（位移与速度）和气动载荷的函数。针对这类方程,本文尝试引入精细积分法及其衍生格式,借助数值方法计算Duhamel积分项。从积分精度与数值稳定性方面比较研究具有代表性的精细库塔法和高精度直接积分法。结合隐式积分算法,评估精细积分法应用于旋翼动力学方程的可行性。算例表明,精细积分法对矩形直桨叶动力学方程具有足够的求解精度。     

Flooding in urban drainage systems: coupling hyperbolic conservation laws for sewer systems and surface flow

In this paper, we propose a model for a sewer network coupled to surface flow and investigate it numerically. In particular, we present a new model for the manholes in storm sewer systems. It is derived using the balance of the total energy in the complete network. The resulting system of equations contains, aside from hyperbolic conservation laws for the sewer network and algebraic relations for the coupling conditions, a system of ODEs governing the flow in the manholes. The manholes provide natural points for the interaction of the sewer system and the runoff on the urban surface modeled by shallow‐water equations. Finally, a numerical method for the coupled system is presented. In several numerical tests, we study the influence of the manhole model on the sewer system and the coupling with 2D surface flow. Copyright © 2014 John Wiley & Sons, Ltd.