介质与结构三维动力相互作用分析的半解析边界元—半解析有限元结合法

本文将半解析边界元一半解析有限无结合法用于介质与结构的动力相互作用研究:用半解析边界元法分析具有复杂地表面的半无限介质,用半解析有限元法分析具有任意截面形状的柱体结构,利用介质与结构交界面上的位移相容条件和力平衡条件,将介质与结构联系起来。联立京解上述半解析边界元方程和半解析有限元方程,对应每一时间步进,可同时求出介质与结构交界面上的位移、速度、加速度和相互作用力以及地表面的运动情况.与目前广泛研究的边界元—有限元结合法相比,本方法在介质与结构二个个区域各降低了一维空间,因而离散单元数和计算工作量大幅度减少,人工输入数据非常简单.文中还考虑了地下结构的长跨比效应、厚度效应和介质效应.     

地下结构与岩体动力相互作用的一种解析解

本文根据大量试验和数值分析结果指出:在侧向爆荷下岩洞在厚度为跨度三分之一围岩中具有厚壁受弯构件的力学特征,而在该围岩区外即基本上接近自由场应力状态,并可用厚板理论方程在自由场压力的外载下进行求解.因此,地下结构与围岩动力相互作用,可用分别代表衬砌及介质的基于薄板与厚板理论的受弯构件动力方程宋描述.围岩和衬砌二者之间的相互作用力用接触压力函数q(x,t)加以联系.通过解一组联立方程,给出了计入与弹性半空间相互作用效应的直墙拱顶衬砌时动力分析的解析解,同时列出了函数q(x,t)的解析表达式. 本解析解将有助于从理论上探讨地下结构与介质动力共同作用的一些本质问题.     

深分层流体中内孤立波的相互作用——Ⅰ.弱相互作用 *

采用Lagrange观点研究分层流体中内孤立波的弱相互作用,它包括不同模式孤立波间的追撞和迎撞,以及相同模式孤立波间的迎撞.分析表明在有限深度情形每个波遵循ILW方程,而在无限深度情形每个波满足Benjamin-Ono方程,相互作用的主要效应体现在相移上.     

CFD-半解析模型混合的管束结构流弹失稳预测方法

横向流作用下管束结构传统流弹失稳模型的建立或多或少需要获取实验流体力参数作为输入条件.因此非常需要开发一种不依赖实验数据的管束结构流弹失稳模型.该文提出了一种改进的CFD仿真与半解析方法混合的管束结构流弹失稳预测方法.采用CFD仿真方法获取半解析模型中关键的相位延迟函数,并根据速度将其表示为简单的分段函数.最终预测了横向流作用下间距比为1.375的平行三角形与正三角形管束结构的流弹失稳阈值,预测结果与文献中的实验结果吻合良好.该文提出的CFD-半解析模型混合方法同样适用于其他管束结构的流弹失稳预测,为蒸汽发生器传热管流弹失稳现象的研究提供了一种时间成本较低的预测方法.     

液晶流体的半强解

该文将证明,即使初始密度在Ω中没有正下界,二维向列液晶流体存在半强解.该文主要的新颖点在于新估计||аtd||_(L4/3)(I,L~2(Ω))不依赖于p的下界,其中d及ρ分别表示流体的密度与分子方向.     

基础动力分析的一种半解析、半数值方法

提出了一种基础动力分析的半解析、半数值计算方法．采用Lamb解及其相应的近似公式,建立了基础动反力和位移的关系式．从而可象静力问题那样将基础板分离出来,将板看作上部作用已知载荷,下部作用用挠度表示的地基反力,因此只需要对板进行有限元分析．采用这种方法分析了不同形状、 不同刚度、不同频率下的地基板的振动问题, 而且可以考虑基础埋深的影响．算例分析表明,提出的方法是一种计算简便、精度较高、适用范围广泛的有效数值方法．     

关于流体问题的混合有限元方法

本文对流体力学中解偏微分方程的混合有限元方法进行研讨．并考虑位势流体方程和不可压粘性流体方程为例．提出其理论结果与误差。     

四段式有限元法分析热耦合的流体-固体相互作用问题

给出了一种流(体)-热-结构综合的分析方法,固体中的热传导耦合了粘性流体中的热对流,因而在固体中产生热应力.应用四段式有限元法和流线逆风Petrov-Galerkin法分析热粘性流动,应用Galerkin法分析固体中的热传导和热应力.应用二阶半隐式Crank-Nicolson格式对时间积分,提高了非线性方程线性化后的计算效率.为了简化所有有限元公式,采用3节点的三角形单元,对所有的变量:流体的速度分量、压力、温度和固体的位移,使用同阶次的插值函数.这样做的主要优点是,使流体-固体介面处的热传导连接成一体.数个测试问题的结果表明,这种有限元法是有效的,且能加深对流(体)-热-结构相互作用现象的理解.     

湍流相干结构与小尺度结构之间的相互作用

本文首先对切变湍流场中存在大尺度相干结构与小尺度结构和不同尺度结构之间的相互作用进行了试验研究,得到了一些特征值,其次,在试验的基础上,建立了考虑不同尺度结构之间的相互作用后相干结构的数学描述和模式识别方法,并对光滑壁面与均匀密集加糙壁面条件下湍流边界层中的相干结构进行了模式识别。结果表明,文中所建立的计算方法是可行的。     

A Semi-Analytical Method of Solving the Fokker-Planck-Equation for High-Dimensional Nonlinear Mechanical Systems

Stochastic processes are a common way of describing systems that are subjected to random influences. Technical systems may be excited by road roughness or wind gusts, for example, as well as fluctuating system parameters, which can all be described by stochastic differential equations. In previous works by the author and others (see [1], for example) it has been demonstrated how a Galerkin-method can be used to obtain global numerical solutions of the Fokker-Planck-Equation (FPE) for nonlinear random systems. Computational efforts are reduced by orthogonal polynomial expansion of approximate solutions so that probability density functions (pdfs) for comparably high-dimensional problems have been computed successfully. Stationary mechanical systems with dimensions up to d = 10 have been investigated, including polynomial as well as non-smooth nonlinearities. This article presents results for different energy-harvester-systems under stochastic excitation, a field of research that has become the subject of increasing attention in the last years. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

混凝土断裂力学虚拟裂缝模型的半解析有限元法

利用平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,以解析的方法推导出基于混凝土断裂力学中虚拟裂缝模型的平面裂纹解析元列式．将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和荷载混凝土平面裂纹的虚拟裂缝模型计算问题．数值计算结果表明方法对该类问题的求解是十分有效的,并有较高的精度．     

A New Gradient Method for Ill-Posed Problems

In this paper, we present a new gradient method for linear and nonlinear ill-posed problems F(x) = y. Combined with the discrepancy principle as stopping rule it is a regularization method that yields convergence to an exact solution if the operator F satisfies a tangential cone condition. If the exact solution satisfies smoothness conditions, then even convergence rates can be proven. Numerical results show that the new method in most cases needs less iteration steps than Landweber iteration, the steepest descent or minimal error method.     

A Decomposition Method for Some Biharmonic Problems

In this paper we consider two biharmonic problems [13] which will be conventionally indicated as "simply supported" and "clamped plate" problem. We construct a decomposition method [16], [19] related to the partition of the plate in two, or more, subdomains. We carry on the numerical treatment of the method first decoupling these fourth order problems into two second order problems, then discretizing these problems by mixed linear finite element and obtaining an algebraic system. Moreover, we present an iterative block algorithm for solving the foregoing system, which can be efficiently developed on parallel computers.In the end, we extend the method to the respective biharmonic variational inequalities [10].     

A Two-Level Method for Nonsymmetric Eigenvalue Problems

A two-level discretization method for eigenvalue problems is studied. Compared to the standard Galerkin finite element discretization technique performed on a fine grid this method discretizes the eigenvalue problem on a coarse grid and obtains an improved eigenvector (eigenvalue) approximation by solving only a linear problem on the fine grid (or two linear problems for the case of eigenvalue approximation of nonsymmetric problems). The improved solution has the asymptotic accuracy of the Galerkin discretization solution. The link between the method and the iterated Galerkin method is established. Error estimates for the general nonsymmetric case are derived.     

Stokes问题的区域分解法

本文主要讨论了Ｓｔｏｋｅｓ问题的非重迭型两仓区域性情形的区域分解算法，首先讨论了连续情形，然后将区域分解算法应用到Ｓｔｏｋｅｓ问题的非协调离散情形。     

A Continuous Method for Convex Programming Problems

In this paper, we present a continuous method for convex programming (CP) problems. Our approach converts first the convex problem into a monotone variational inequality (VI) problem. Then, a continuous method, which includes both a merit function and an ordinary differential equation (ODE), is introduced for the resulting variational inequality problem. The convergence of the ODE solution is proved for any starting point. There is no Lipschitz condition required in our proof. We show also that this limit point is an optimal solution for the original convex problem. Promising numerical results are presented.This research was supported in part by Grants FRG/01-02/I-39 and FRG/01-02/II-06 of Hong Kong Baptist University and Grant HKBU2059/02P from the Research Grant Council of Hong Kong.The author thanks Professor Bingsheng He for many helpful suggestions and discussions. The author is also grateful for the comments and suggestions of two anonymous referees. In particular, the author is indebted to one referee who drew his attention to References 15, 17, 18.     

A Method for Solving Crew Scheduling Problems

The method discussed provides an allocation of jobs to men in a transportation system. Each man is assigned a prespecified shift, associated with a base station, and returned to his base station at the end of his shift. The total number of men required is minimized, subject to a minimum time between jobs, a suitable lunch break, and the performance of all the jobs, employing the decomposition principle of linear programming.