两类弱非线性振动微分方程的插值摄动解法

本文分别用插值摄动法的两种不同方法（第一,第二解法）求解了两类弱非线性振动问题,用第二解法得到的Ｄｕｆｆｉｎｇ方程的解,精度很高,当小参数不是很小时,甚至比Ｌ－Ｐ法的结构更加精确,用第一解法求解有阻尼的自由振动问题时,由于可以公式化,故求解过程十分简便,本文选取的初始零级近似解,具有新的特色。     

强迫范德波振荡的全局分岔的过渡区

本文研究强迫范德波振范在一指定参数平面内的分岔结构，参数平面内特别地包含中等参数域；单个亚谐解１／（２Ｋ＋１）的主模态锁定区顺序排列，并且由地渡区相间隔是分岔的主要结构；提示了有两类过渡区，（１）简单的，牲介转动数为１／（２Ｋ＋１）的两个模态锁定解共存；（２）复杂的，其中模态锁定觚发子区的解的转 是介于１／（２Ｋ＋１）和１／（２Ｋ－１）之间的分数以及准周期、混沌解的存在，并发生鞍结分岔、对称破缺分     

无限无与相同子结构串的一致性及其算法

讨论了无限元方法（１）与相同子结构串分析（２）的致性，综合文（１）和（２）得到一种通用算法，依据文（３）尚可应用于ＬＱ控制问题，且提出一种直接求出转移矩阵的算法，具有简便和较高精度的优点。     

用能量法分析层状材料弹性接触问题

利用能量法分析了层状材料（薄膜／基体）弹性接触问题，得到了具有一阶精度的闭合解，给出了求解薄膜弹性模量和泊松比的表达式，并与有限元的数值解进行了比较。二者比较结果表明：在工程材料范围内，理论解与数值解相差在6％以内；同时表明单相材料中剪切模量与弹性模量之间的关系也适用层状材料中的薄膜材料。在数值解的基础上，讨论了薄膜厚度与压头半径的比值对求解精度的影响，发现此比值对精度影响不大。通过对层状材料等效泊松比与等效弹性模量的定义，给出了用压痕实验测定薄膜泊松比与弹性模量的方法。     

周期桶状垫圈全平面应变问题

本文运用Ｍｕｓｋｈｅｌｉｓｈｖｉｌｉ复变方法研究周期桶状垫圈全平面应变问题。将此特殊的三维弹性问题归结为求解三个复应力函数所满足的解析函数边值问题。对相同材料和不同材料（但μ￣＋＝μ￣－）两类问题分别进行了讨论,并获得了其封闭解。     

两种浸入式边界方法的比较

介绍两类不同的浸入式边界方法及其对它的改进. 然后采用均匀矩形交错网格和压力校正投影法,对不可压流场中的二维圆柱绕流进行了数值求解并对比了两类方法的精度.计算分析表明,连续显力法具有构造简单,适用性强的优点. 但离散隐力法在物面边界精度上要优于前者. 改进后,在二阶精度的离散格式下物面边界精度较低的显示力源法的精度有一定提高,同时发现,加密网格以提高数值精度的方法对于连续显力法并不总是有效.而同样格式下,离散隐力法具有更高精度,其中预测-校正离散隐力法可以在此基础上获得更小的计算误差和更快的收敛速度. 数值解与文献已有的数值和实验结果吻合得很好,表明边界算法及其程序是可靠和有效的.      

等截面梁有限变形的传递函数解法

本文应用传递函数方法对等截面梁的有限变形进行了分析,对于等截面梁的有限变形问题,该方法从变分方程出发把问题表述为状态空间的形式,然后利用Gauss积分对轴力进行加速迭代求解,不需要进行增量迭代即可取得具有良好计算精度的数值结果,对简单受力的等截面梁情况该解可以看作是所讨论问题的精确解。对于受力比较复杂或者阶梯变截面梁情况,为减少运算量,可以和有限元法类似,采用多个单元进行拼接,从而得到问题的解。数值算例表明,本方法具有半解析、精度高、收敛快等特点。     

研究材料动态本构特性中的重要作用

在材料动态本构关系的研究中，不论是由波传播信息反求材料本构关系，即所谓解第二类反问题，还是利用应力波效应和应变率效应解耦的方法（如SHPB技术），应力波传播实际上都起着关键作用。在一般性讨论的基础上，就SHPB试验技术分析了应力波传播如何影响材料动态本构特性的有效确定。对于应力/应变沿试件长度均匀分布假定以及一维应力波假定，着重进行了分析。     

插值摄动法及其在力学中的应用

本文研究了最高阶导数乘以小参数，或出现奇点的微分方程的定解问题，用插值摄动法求得了一级近似解，它和通常的奇异摄动法（匹配法、多尺度法）的一级近似解的精度相同。     

一种适用于简支多边形薄板问题的有限单元法

简支多边形薄板双调和定解问题可分解为二个互不耦合的Ｐｏｉｓｓｏｎ方程的定解问题，通过比拟，可用二维平面应力（应变）单元进行有限元分析。数值算例表明，本文采用的方法在较粗的网格下即可得到较高的精度，而且具有速度快、占用计算机内存少等优点。     

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy.     

Controlled random search technique for estimation of convective heat transfer coefficient

This paper is concerned with a method for solving inverse heat conduction problem. The method is based on the controlled random search (CRS) technique in conjunction with modified Newton–Raphson method. The random search procedure does not need the computation of derivative of the function to be evaluated. Therefore, it is independent of the calculation of the sensitivity coefficient for nonlinear parameter estimation. The algorithm does not depend on the future-temperature information and can predict convective heat transfer coefficient with random errors in the input temperature data. The technique is first validated against an analytical solution of heat conduction equation for a typical rocket nozzle. Comparison with an earlier analysis of inverse heat conduction problem of a similar experiment shows that the present method provides solutions, which are fully consistent with the earlier results. Once validated, the technique is used to investigate another estimation of heat transfer coefficient for an experiment of short duration, high heating rate, and employing indepth temperature measurement. The CRS procedure, in conjunction with modified Newton–Raphson method, is quite useful in estimating the value of the convective heat-transfer coefficient from the measured transient temperature data on the outer surface or imbedded thermocouple inside the rocket nozzle. Some practical examples are illustrated, which demonstrate the stability and accuracy of the method to predict the surface heat flux.     

Effects of outflow boundary condition on convective heat transfer with strong recirculating flow

Three practices of treating outflow boundary condition were adopted in computations for convective heat transfer of a two-dimensional jet impinging in a rectangular cavity. The three practices were local mass conservation method, local one-way method and fully developed assumption. The numerical solutions of the three methods were compared with test data obtained via, naphthalene sublimation technique. It was found that the fully developed assumption was inappropriate, and the local one-way method could provide reasonably good results for the cavity bottom, while for the lateral wall the results with this method qualitatively differed from the test data. The solution with the local mass conservation method was the best. It thus suggested that for a problem expected with a strong recirculating flow at the exit of the computation domain, the local mass conservation method be adopted to treat the outflow boundary condition.     

Lattice‐Boltzmann and meshless point collocation solvers for fluid flow and conjugate heat transfer

The applicability and performance of the lattice‐Boltzmann (LB) and meshless point collocation methods as CFD solvers in flow and conjugate heat transfer processes are investigated in this work. Lid‐driven cavity flow and flow in a slit with an obstacle including heat transfer are considered as case studies. A comparison of the computational efficiency accuracy of the two methods with that of a finite volume method as implemented in a commercial package (ANSYS CFX, ANSYS Inc., Canonsburg, PA) is made. Utilizing the analogy between heat and mass transfer, an advection–diffusion LB model was adopted to simulate the heat transfer part of the slit flow problem followed by a rigorous mapping of the mass transfer variables to the heat transfer quantities of interest, thus circumventing the need for a thermal LB model. Direct comparison among the results of the three methods revealed excellent agreement over a wide range of Reynolds and Prandtl number values. Furthermore, an integrated computational scheme is proposed, utilizing the rapid convergence of the LB model in the flow part of the conjugate heat transfer problem with that of the meshless collocation method for the heat transfer part. The meshless treatment remains sufficiently rapid even for conduction‐controlled processes in contrast to the LB method, which is very rapid in the convection‐controlled case only. A single, common computational grid, composed of regularly distributed nodes is used, saving significant computational and coding time and ensuring convergence of the discrete Laplacian operator in the heat transfer part of the computations. Copyright © 2012 John Wiley & Sons, Ltd.     

提高多体系统离散时间传递矩阵法计算精度的研究

深入探讨多体系统离散时间传递矩阵法对平面、空间刚体-光滑铰多体系统运动响应的研究。提出提高该方法计算精度和计算稳定性的方法，导出相应的多端刚体传递矩阵。设计了角坐标的迭代循环，该变量不必采用近似形式，因而提高了计算精度和计算稳定性。其它方法有：1)增加泰勒展开式的高阶项；2)合理选择将速度、加速度表示为位移的线性函数的方法(本文简称线性化方法)；3)合理确定迭代循环的初值等。对4种多体系统进行了计算机仿真研究，表明本文提出的方法有效。     

Analytical solution of the spherical indentation problem for a half-space with gradients with the depth elastic properties

The contact problem for the impression of spherical indenter into a non-homogeneous (both layered and functionally graded) elastic half-space is considered. Analytical methods for solving this problem have been developed. It is assumed that the Lame coefficients vary arbitrarily with the half-space depth. The problem is reduced to dual integral equations. The developed methods make it possible to find the analytical asymptotically exact problem solution, suitable for a PC. The influence of the Lame coefficients variation upon the contact stresses and size of the contact zone with different radius of indenter as well as values of the impressing forces are studied. The effect of the non-homogeneity is examined. The developed method allows to construct analytical solutions with presupposed accuracy and gives the opportunity to do multiparametric and qualitative investigations of the problem with minimal computation time expenditure.     

Modeling and Application of Gas Pressure Measurement in Water-Saturated Coal Seam Based on Methane Solubility

The unconfined seepage problem is a classic moving boundary problem, in which the position of phreatic surface is unknown at the beginning of solution and should be determined through iteration. Mesh-free methods are especially suitable for solving this problem. In this work, the moving Kriging mesh-free method with Monte Carlo integration is proposed. Additionally, a corresponding procedure for handling material discontinuity is presented, which extends the approach to inhomogeneous medium. The present method is a true mesh-free method, which does not require a mesh for either shape function construction or numerical integration. Another advantage of the present method is the convenient numerical implementation. Numerical examples show that the present method can achieve better convergence and higher accuracy with rational computation cost when compared with the original mesh-free method. The present method is also verified to be applicable in analyzing transient seepage through homogeneous and inhomogeneous media.     

数值模拟在钱塘江涌潮分析中的应用──Ⅱ.计算结果和分析

关于钱塘江涌潮分析中用数值模拟的计算结果和分析,对于一维情况,采用有精确解问题的计算、水跃的数值模拟和溃坝的数值模拟来检验数值方法的正确性,并将该方法应用于钱塘江涌潮的计算．对于二维情况,对存在理论解的直道水激波与有实验数据的湾道溃坝和非线性水波爬坡问题进行了计算,并将该方法应用于钱塘江涌潮的计算,数值计算结果表明了方法的有效性．     

快速求解叶栅流动的边界元方法

本文利用边界元方法，通过ｋｒｉｃｈｈｏｆｆ变换将描述叶栅流动的控制方程转换成线性方程。并将广义ｋ－Ｊ条件与边界积分方程联立求解，避免了非线性项和叶片出气角的迭代计算。完成了一种快速求解任意迥转面叶栅流场的计算程序，实用表明与其它数值方法及实验结果符合较好，具有快带、简明、实用的特点。     

Transient Solution for the Energy Balance in Porous Media Considering Viscous Dissipation and Expansion/Compression Effects Using Integral Transforms

Monitoring of downhole flowing temperatures in oil wells is gaining attention in the recent years due to the possibility of exploring these data for reservoir characterization and determination of inflow profiles along the well completions, leading to an increased interest in the development of solutions for the equations governing the thermal behavior of a reservoir. In this work, it is proposed to use the generalized integral transform technique (GITT) to provide solutions for the energy balance equation, considering the thermal effects related to fluid flow. A formal and general solution for the energy balance in the porous media is presented and validated. It is presented the application of the proposed solution to one-dimensional and two-dimensional problems in the Cartesian coordinate system. The two-dimensional problem, which considers heat transfer to the surrounding impermeable formations, is tackled by a single domain formulation. The mathematical approach taken in these solutions is rigorous, valid for all flow regimes (transient, late-transient and pseudo-steady-state/steady-state) and for any orthogonal coordinate system, presenting the possibility of achieving differentiable and stable solutions with controlled accuracy. The solution comprises an important contribution to support the application of temperature data to reservoir engineering problems.