夹层板弯曲问题的Hoff理论的解析解

本文根据Ｈｏｆ提出的夹层板理论和胡海昌、柳春图对该理论的简化理论，提出了矩形夹层板弯曲问题的解析解的一般格式，它可以用于求解各种边界条件下矩形夹层板弯曲问题的Ｈｏｆ理论的解析解。从而，使得考虑表层抗弯刚度的矩形夹层板弯曲问题求解格式化。     

资源约束条件下工期最短问题研究

本文对资源约束条件下的工期问题进行了深入研究,从解析法到启发式算法,对这些方法取得效果和存在的问题都进行了剖析,尤其是对启发式算法的研究,最后作者表达了对该问题的研究观点。     

求解声学问题的元胞自动机方法

为探究元胞自动机(cellular automata, CA)方法在求解声学问题中的适用性,结合CA原理与声波方程导出一维平面波场CA的局部演化规则,构建出一维声学CA模型,并计算不同边界条件下声管内的声压分布,同时对比解析解验证模型的正确性;以球坐标下的声波方程为基础,推导出脉动球源Y函数的CA局部演化规则,进而建立二维声学CA模型;利用该模型探讨脉动球源声辐射规律,并将分析结果与解析解进行对比。结果表明:所建立的声学CA模型能准确模拟平面波场与球面波场声辐射规律,且结果与解析解吻合程度高;该CA模型可避免传统CA模型中元胞状态各向异性更新的问题;对于双球源组合声场,该CA模型依旧具有良好的适用性。     

DGH方程Cauchy问题解的解析性

Cauchy问题是偏微分方程研究中的重要问题之一，而初值的性质在很大程度上决定了偏微分方程解的性质。本文研究了DGH方程的Cauchy问题在初值解析的情形下解的性质：我们在一个合适度量的Banach空间中利用压缩的思想证明，DGH方程Cauchy问题初值解析时，其解关于空间变量全局解析，而关于时间变量局部解析。     

弹性矩形薄板弯曲问题的一个解法

本文建立一个关于弹性矩形薄板弯曲的解析解法。该方法适用于求解任意荷载及边界条件下矩形薄板的弯曲问题，特别是对具有边梁支承的矩形板，更显示出特有的优越性。     

各向异性材料平面问题基本解析解的特征方程解法

该文提出了一种利用特征方程解法构造基本解析解的新方法,并将其应用到各向异性材料平面问题,成功构造了完备且独立的系列基本解析解.构造各向异性材料平面问题控制微分方程的算子矩阵,通过其行列式计算可得到问题特征通解所需满足的特征方程,将所求得特征通解代入到微分方程算子矩阵所对应的伴随矩阵,可推导得出各向异性材料平面问题的基本解析解.根据基本解析解独立性的论证,可得到系列独立且完备各向异性材料平面问题基本解析解.利用特征方程解法求解基本解析解思路简单、并且容易找到独立且完备的解析解,其结果可以成为相关数值计算方法的基础.     

DGH方程Cauchy问题解的解析性（英文）

Cauchy问题是偏微分方程研究中的重要问题之一,而初值的性质在很大程度上决定了偏微分方程解的性质.本文研究了DGH方程的Cauchy问题在初值解析的情形下解的性质:我们在一个合适度量的Banach空间中利用压缩的思想证明,DGH方程Cauchy问题初值解析时,其解关于空间变量全局解析,而关于时间变量局部解析.     

具有边梁的悬臂矩形板的弯曲问题

本文建议一个求解具有边梁悬臂矩形板弯曲问题的解析解法。该法将有边梁和无边梁悬臂矩形板弯曲问题的解融为一体，在有边梁悬臂矩形板的解中令边梁弯曲刚度为零即得到无国梁悬臂矩形板的解。     

解析试函数法分析平面切口问题

本文利用平面切口问题的基本解析解构造单元,分析平面切口问题。通过分析平面切口问题的Williams特征方程的有解区间,使用分区加速lleruM&&法依序无漏地计算了平面V型切口特征值。从Williams应力函数出发,推导了V型切口尖端的应力场基本解析解列式。并用此根据分区混合能量原理构造了含切口解析单元ATF-VN的刚度矩阵。文中还对含切口解析单元的单元尺寸和应力项数等因素对分析结果的影响进行了系统的讨论。     

层状正交各向异性材料弹性波导问题的数值计算

研究复合材料弹性波导问题的数值计算方法。将问题导向哈密顿体系,在哈密顿体系中以位移向量和应力向量综合成全状态向量,在杂交体系中建立动力-部分杂交元,导出一套哈密顿体系下新的半解析法。本文中给出了该方法在分层正交各向异性材料的弹性波导问题的数值算例。计算结果展现了该方法在弹性波导问题的应用前景。     

PROCEDURES FOR SOLVING SINGLE-PASS STRIP LAYOUT PROBLEMS

Strip layout is an important step in the planning of operations using blanking dies. Typically the strip layout problem has been resolved using methods which provide approximate solutions, since it is viewed as a class of general 2-D nesting problem which is NP-Hard. This implies that we need to investigate special cases of the strip layout problem that will permit polynomial running time algorithms, while having some practical application in processes of cutting shapes from sheet stock. In this paper we present an exact procedure with polynomial running time for die single-pass single-row layout problem. This problem tries to layout identical shapes on a strip that will go thorough a single row die only once, such as to maximize die number of parts to be yielded by the strip. The paper investigates this problem for two cases: the case for which die width of die strip is larger than any possible orientation of the part, and the case for which the width of die strip is restricted so mat not every orientation is feasible. We also consider the problem of cutting a sheet of metal into strips so as to maximize die sum of me parts yielded by each sheet.     

HEURISTIC NONSERIAL DYNAMIC PROGRAMMING FOR LARGE PROBLEMS

Dynamic programming is an extremely powerful optimization approach used for the solution of problems which can be formulated to exhibit a serial stage-state structure. However, many design problems are not serial but have highly connected interdependent structures. Existing methods, for the solution of nonserial problems require the problem to possess a certain structure or limit the size of the problem due to storage and computational time requirements. The aim of this paper is to show that nonserial problems can be solved by the use of dynamic programming incorporating algorithms based on heuristics. Two such algorithms are developed using artificial intelligence concepts of estimating the likelihood of future results on present decisions. The algorithms are explained in detail, A small problem is solved and the results of testing them on large scale problems are given. The method is then used to solve a problem drawn from the literature.     

偶应力反问题参数识别

利用有限元技术和最小二乘原理,建立了便于敏度分析的偶应力反问题数值求解模型,并采用高斯牛顿方法进行求解。模型考虑了材料的非均质、各向异性等因素,并在计及测量误差的情形下,对其进行了数值验证,得到了令人满意的结果。此外,还通过反问题的求解,对偶应力本构等效的网格材料的等效本构参数进行了估算,并给出相应算例。     

A NEW APPROACH TO NONLINEAR MIXED DISCRETE PROGRAMMING PROBLEMS

Abstract

In this paper a novel method is developed for the numerical solution of a non-linear mixed discrete programming problem. The problem is first transformed into another mixed zero-one discrete optimization problem by replacing each of the discrete variables by a set of new variables with a linear constraint. Each of the new discrete variable sets is then made continuous on [0,1] by introducing a quadratic constraints. Thus the original mixed discrete problem is transformed into a continuous nonlinear optimization problem with constraints. The numerical experiments, performed to demonstrate the effectiveness of the method, show that the method is superior to the previous ones.     

双曲传热反问题研究

该文建立了双曲妈传热正/反问题求解模型,应用高斯-牛顿方法,对辐射边界进行了识别.空间上采用等参元进行离散,时域上采用时域精细算法进行离散,利用测量信息和计算信息构造最小二乘函数,将多宗量反演识别问题转化为一个优化问题,所建模型可对导热系数和辐射边界等宗量进行有效的单一和组合识别.给出了相关的数值验证,对信息测量误差作...     

断裂问题的特征根区间及其二分迭代求解

本文对任意切口和任意边界条件的双材料反平面问题和单材料平面问题的特征方程进行了分析研究，给出了这两类问题的各阶特征根分布区间，从而易于利用一般的迭代法进行高效可靠的求解．本文利用二分法研制了相应的通用特征根求解器，可供任何数值方法直接调用．文中给出了若干数值算例用以显示本法的可靠性、高精度和高速度等优点．     

STEINER PROBLEMS IN GRAPHS: ALGORITHMS AND APPLICATIONS

Consider an undirected graph G = (V, E) with positive edge weights and a nonempty set S ? V, where Vand E are the sets of vertices and edges of G respectively. The Steiner problem in graphs is that of finding a subgraph of G which spans S and is of minimum total edge weight. In this paper we survey solution procedures for this problem. As the associated decision problem is NP-Complete we place special emphasis on heuristic methods of solution. We also examine special cases, related problems, and applications. The paper concludes with ideas for the development of new, efficient heuristics.     

钢筋混凝土板弯曲问题的各向同性化域外奇点解法

本文提出了求解钢筋混凝土板弯曲问题的各向同性化域外奇点法。引入简单的坐标变换，将该问题转化成相应的各向同性板的弯曲问题，利用后者的简单格林函数，按域外奇点法求解。算例表明，这种方法简单，计算时间短，精度高。     

用初参数法解多层地基的动力问题

本文应用Ｆｏｕｒｉｅｒ积分变换，求出平面多层地基动力问题的初参数解，这些公式简单明了，便于数值计算，不论弹性层数目多少，都不必求解联立方程。