广义变分原理的结构形状优化伴随法灵敏度分析

提出了一种利用伴随变量进行结构形状优化灵敏度分析的新方法. 基于广义变分原理,考虑了形状优化中位移边界条件的变化对结构响应的影响. 新方法弥补了Arora等人所提出的形状优化灵敏度分析变分原理中的缺陷,为采用伴随法进行灵敏度分析提供了新的框架.     

瞬态热传导方程精细积分方法中对称性的利用

采用精细积分法求解瞬态热传导方程时,对指数矩阵进行变换后使其具有对称性,利用这一特性可使存贮量和计算量降低一半。变换后指数矩阵的带宽特性不变,采用子域精细积分可进一步提高算法的计算与存储效率。     

获得热传导问题“拟解析解”的精细积分算法

研究并讨论了用于热传导分析有限元解的精细积分算法，算法很好地克服了传统方法求解时的单调性问题，且对空间离散后所获得方程的解是解析的，因而算法的解将具有“拟解析解”的意义，论文证明了算法单调性．     

瞬态热传导问题的精细积分数值流形方法研究

数值流形方法（NMM）因其特有的双覆盖系统（数学覆盖和物理覆盖）在域离散方面具有独特的优势,而精细时间积分法则具有精度高、无条件稳定、无振荡以及计算结果不依赖于时间步长等特点。发展了用于研究二维瞬态热传导问题的精细积分NMM。结合待求问题的控制方程和边界条件,并基于修正变分原理导出了NMM的总体方程,给出了求解此类时间相依方程的精细时间积分及空间积分策略,选取了两个典型算例对方法的有效性进行了验证,结果表明本文方法可以高效高精度地求解瞬态热传导问题。     

线性常微分方程灵敏度分析的精细积分法

利用指数矩阵的导数计算来求解一类一阶线性常系数微分方程组对某一设计变量的灵敏度计算问题。对于初值问题,利用指数矩阵的导数,递推得到状态向量的灵敏度;对于线性两点边值问题,通过两点之间的状态向量的导数关系,得到全部初始条件,进而转化为初值问题计算。指数矩阵及其导数阵的高精度计算基于2N类算法,在此基础上可实施灵敏度分析的计算。本文给出了初值和两点边值常微分方程的高精度灵敏度计算方法,计算结果可认为是计算机上的精确解,算例验证了算法的有效性。     

材料热传导系数随温度变化函数的反演方法

材料热传导系数的反演是一类典型的热传导逆问题。针对材料热传导系数随温度变化的情况,本文将材料的热传导系数值按温度区间分段离散,建立了通过材料边界点的温度测量来反演各温度区间热传导系数值的遗传算法和伴随方程法。通过典型算例分析和考虑测量噪声、系统噪声的反演计算结果分析表明：所建立的两种反演算法都是可行有效的,受测量随机噪...     

一种新的形状灵敏度分析方法——具有两类变量的伴随方程法

本文将所考虑的问题视为具有两类独立变量的力学系统,通过建立具有两类变量的伴随系统方程,得到了定义在变化边界上的目标或约束泛函的敏度分析公式,由此建立了完全边界型的形状优化方法。     

轴对称热传导有限元格式

分析了目前一些有限元专著中轴对称热传导有限元方程推导中的问题,给出了轴对称热传导有限元格式的正确表达形式.     

非均质材料热传导问题的扩展有限元法

针对非均质材料,提出了以导热系数为基本参数的热传导扩展有限元法。划分网格时不需要考虑材料界面的存在,因此网格的形成可以大大地简化,且可以获得高质量的网格。不含材料界面的单元,其温度场函数将退化为常规有限元的函数。含材料界面的单元,采用基于水平集的加强函数加强常规温度的近似,加强函数用于模拟界面。数值算例结果体现了该方法...     

PRECISE INTEGRAL ALGORITHM BASED SOLUTION FOR TRANSIENT INVERSE HEAT CONDUCTION PROBLEMS WITH MULTI-VARIABLES

IntroductionIHCPs (InverseHeatConductionProblems)arecloselyassociatedwithmanyengineeringaspects,andwelldocumentedintheliteratures,coveringtheidentificationsofthermalparameters[1,2 ],boundaryshapes[3],boundaryconditions[4 ]andsource_relatedterms[5 ,6 ]etc .Howeveritseemsthatonlylittleworkisdirectlyconcernedwithmulti_variablesidentificationsbyauthors’knowledge.Tsengetal.presentedanapproachtodeterminingtwokindsofvariables[7],butonlygavefewnumericalexamplestodeterminethemsimultaneously .Thesol…     

An adaptive algorithm of precise integration for transient analysis

This paper presents an improved precise integration algorithm for transient analysis of heat transfer and some other problems. The original precise integration method is improved by means of the inverse accuracy analysis so that the parameterN, which has been taken as a constant and an independent parameter without consideration of the problems in the original method, can be generated automatically by the algorithm itself. Thus, the improved algorithm is adaptive and the accuracy of the algorithm is not dependent on the length of the time step in the integration process. It is shown that the numerical results obtained by the method proposed are more accurate than those obtained by the conventional time integration methods such as the difference method and others. Four examples are given to demonstrate the validity, accuracy and efficiency of the new method. Project supported by the National Natural Science Foundation of China (No. 19872016, 19872017), the National Key Basic Research Special Foundation (G1999032805) and the Foundation for University Key Teachers by the Ministry of Education of China.     

半无限介质瞬态热传导的同伦分析法

In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method （HAM） is applied to solve this problem and analytical results are compared with those of the exact and integral methods results. The results show that the HAM can give much better approximations than the other approximate methods： Changes in heat fluxes and profiles of temperature are obtained at different times and positions for copper, iron and aluminum.     

层合圆柱三维温度场分析的半解析-精细积分法

针对圆柱体的三维温度场分析,提出了一种高效的半解析-精细积分法。将温度场展开为环向坐标的Fourier级数,并对径向坐标进行差分离散,从而把三维热传导方程简化为一系列二阶常微分方程;将这些二阶常微分方程转化为哈密顿体系下的一阶状态方程,并利用两点边值问题的精细积分法求解。由于该方法仅对径向坐标进行差分离散,故相对于传统的数值方法离散规模大幅度减少,不仅提高了计算效率、降低了存贮量,而且缓解了代数方程的病态问题。此外,针对Fourier半解析解,根据热平衡原理推导出了两种材料衔接面的半解析差分方程,从而为求解复合材料层合柱问题打下了基础。算例结果表明,即使对于细长比高达400的圆柱杆件,此方法仍然可以给出精度较高的解答。     

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.     

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method. The English text was polished byYunming Chen.     

A finite element method for the one‐dimensional extended Boussinesq equations

A new finite element method for Nwogu's (O. Nwogu, ASCE J. Waterw., Port, Coast., Ocean Eng., 119 , 618–638 (1993)) one‐dimensional extended Boussinesq equations is presented using a linear element spatial discretisation method coupled with a sophisticated adaptive time integration package. The accuracy of the scheme is compared to that of an existing finite difference method (G. Wei and J.T. Kirby, ASCE J. Waterw., Port, Coast., Ocean Eng., 121 , 251–261 (1995)) by considering the truncation error at a node. Numerical tests with solitary and regular waves propagating in variable depth environments are compared with theoretical and experimental data. The accuracy of the results confirms the analytical prediction and shows that the new approach competes well with existing finite difference methods. The finite element formulation is shown to enable the method to be extended to irregular meshes in one dimension and has the potential to allow for extension to the important practical case of unstructured triangular meshes in two dimensions. This latter case is discussed. Copyright © 1999 John Wiley & Sons, Ltd.