用G'/G-展开法求解相对论Toda格子方程

相对论Toda格子方程描述了格子中在指数形式相互作用力作用下的粒子运动.本文依据齐次平衡原则,利用G'/G-展开法求解出两种形式相对论Toda格子方程组的双曲函数形式孤波解、三角函数形式周期波解和有理函数形式行波解,这些精确解含有较多的任意参数;得到的精确解对格子中在指数形式相互作用力作用下粒子运动的研究具有重要理论价值.     

矩形薄板在随从力作用下的动力稳定性分析

本文用Levy法和有限差分法相结合,研究了两对边简支、另两对边为三种典型支承任意组合的六种弹性矩形薄板在切向均布随从力作用下的动力稳定性问题.通过数值计算,给出各种支承板的失稳形式及相应的临界载荷,并分析了泊松比、板的边长比对板的失稳形式及临界载荷的影响.     

透平内部任意流面非定常粘性流动分析

本文运用张量分析工具,采用原始变量法,导出了透平内部任意流面流动所应满足的偏微分方程,它包含流面的度量张量、第二基本型、主法曲率和Gauss曲率等几何量,充分体现了流面几何结构的内蕴性质与流动方程之间的密切关系.这种方法也表明,用二维问题来逼近三维问题,在理论上和技术上都是可能的. 本文还提出了用两步显式法或分数步长法对有限元方程组求解.     

有姿态角时飞机燃油油量测量技术研究

本文论述了数字式飞机燃油油量测量系统中的一种全新计算方法——“细分—逼近”法的原理和计算过程。该方法借鉴了有限元法的思想,可计算出形状不规则的飞机油箱在任意时刻、任意姿态角组合时的油量。计算程序中采用了符合组合方法,判断油平面与油箱相截的情况。     

目标序列已知的周期波形总失真度的测量

介绍了一种周期性任意波形总失真度的定义及其评价过程和方法,其特点是已知目标波形的数据序列,借助于周期精确测量技术和相关分析实现基波位置参数的精确测量,平移对齐目标波形与测量序列的对应位置后,使用最小二乘法实现任意波形的最优估计,用时域能量方式计算失真,并对测量系统本身的影响进行了补偿.仿真和实验均验证了该方法的正确性及可行性.该方法可用于任意波发生器产生的任意波形失真度的精确测量和计量校准.     

基于镜像法提取多层介质中3D电容参数的研究

提出了一种适用于任意多层电介质分层结构中的3D互连电容参数提取的新方法--反射镜像法.该方法无需对格林函数进行推导,而是根据自由电荷反射原理计算反射镜像的位置和镜像电荷系数从而获得各级镜像分布,继而计算任意多层电介质环境下的3D电容,包括底层或顶层介质接地情况下的3D电容.该方法可克服级数形式的格林函数因受限于电介质分层数目而难以适应大规模集成电路中复杂多变电介质环境下的3D电容参数提取问题.通过对导体面元建立层次式数据结构,这一方法可以利用层次式算法(hierarchical method)实现计算加速.实验证明,该方法能在保证可靠精度的情况下达到迅速收敛,与层次式加速算法结合后,计算效率可达到FastCap法的数倍.     

框─剪体系无连续化假定的简化算法

本文不用连续化假定对任意层高且受任意水平力的框剪体系进行分析，而以Ｂ样条函数结合配点法直接求解框剪间有限个作用力与力矩，导出的递推公式对任意水平荷载可直接应用。经算例并与他法比较表明，本法结果是可信的，且比用连续化假定的方法误差要小。     

框─剪体系无连续化假定的简化算法

本文不用连续化假定对任意层高且受任意水平力的框剪体系进行分析，而以Ｂ样条函数结合配点法直接求解框剪间有限个作用力与力矩，导出的递推公式对任意水平荷载可直接应用。经算例并与他法比较表明，本法结果是可信的，且比用连续化假定的方法误差要小。     

基于基面力概念的余能原理任意网格有限元方法

利用基面力概念,给出一种任意形状网格都可以使用的柔度矩阵表达式的具体形式,运用拉格朗日乘子法得到以基面力为基本未知量的余能原理有限元支配方程,提出计算节点位移的表达式,编制出相应的任意网格有限元计算程序。该文对不同形状的单元网格以及畸变网格进行了计算分析,并与理论解和传统的有限元进行了对比和讨论。结果表明:该方法可以适用于任意形状的有限元网格,对网格的畸变不敏感。     

层合开口桩壳热应力问题的解析解

基于具有任意混合边界条件的Hellinger－Reissner广义变分原理,在柱坐标系下,导出正交各向异性层合开口柱壳混合状态方程和边界条件算子方程的弱形式,建立了层合开口柱壳的热应力混合方程,化混合方程为Hamilton正则方程,在求解中利用Hamilton矩阵的性质和矩阵传递法,保证了层间应力和位移的连续性,给出了任意厚度层合开口柱壳在热荷载和机械荷载共同作用下的解析解。本文提出的方法弱化了求解方程,物理概念清晰,无需特殊技巧,具有一般性和便于推广。本文也为验证其它数值方法的正确性和计算精度提供了考题和依据。     

A new method for solving single and multi-objective fuzzy minimum cost flow problems with different membership functions

Several authors have proposed different methods for solving fuzzy minimum cost flow (MCF) problems. In this paper, some single and multi-objective fuzzy MCF problems are chosen which cannot be solved by using any of the existing methods and a new method is proposed for solving such type of problems. The main advantage of the proposed method over existing methods is that the fuzzy MCF problems which can be solved by using the existing methods can also be solved by the proposed method. But, there exist several fuzzy MCF problems which can be solved only by using the proposed method i.e., it is not possible to solve these problems by using the existing methods. To illustrate the proposed method and also to show the advantages of the proposed method over existing methods some single and multi-objective fuzzy MCF problems which cannot be solved by using the existing methods are solved by using the proposed method and the obtained results are discussed.     

Theoretical study of subregion method and its applications

The theoretical foundation of the subregion method for solving electrostatic and magnetostatic field problems is discussed, and several kinds of subregion methods, including the common combination method, are described. They can be used to solve nonlinear as well as linear field problems. The diakoptical technique is developed and implemented to make the subregion method more effective. Examples are given, showing that (1) more accurate calculations can be made; (2) larger, more complicated problems can be calculated owing to the relatively smaller size of the matrix; (3) the computation time is reduced, especially for nonlinear fields     

Application of integral equations to solving inverse problems of stationary electromagnetic fields

A method of solving inverse problems of stationary electromagnetic fields is described. It can be applied to problems in non-homogeneous, linear and isotropic environments. The method is based on application of integral equations of the first kind which require regularization because they are ill-posed. Numerical calculations of some selected problems confirm the effectiveness of the proposed method.     

Numerical analysis of the influence of residual stresses on crack closure in rings

The stress intensity factors which result when an axially cracked ring containing residual stresses is subjected to an external load have been calculated using a numerical method. When partial crack closure occurs, it has been taken into account. The computations show that residual stresses can cause both cracking problems in service and scatter in experimental data. The method uses a finite-element procedure that is similar to those used with contact problems to provide the basis for a numerical solution. The procedure can be applied to any geometrical configuration that can be analyzed with the finite-element method.     

一种利用有限元反解技术的动态优化设计方法

探讨了将特征值问题的研究成果与传统的优化设计技术相结合以进行结构的动态设计的问题。提出应用有限元模型修正原理及有限元反解技术，将动态性能约束用设计变量显式表达，从而将困难的结构动态优化设计问题转化为普通的数学规划问题，方便于工程应用。实际算例表明，本文提出的方法切实可行     

Body force method

The body force method is based on the principle of superposition. The solution in the body force method is obtained by the superposition of fundamental solutions so as to satisfy a given boundary condition. By means of these fundamental solutions all problems can be solved in principle. In this paper, first the fundamental principle of the body force method is illustrated and then its application to crack problems, elastic–plastic problems and elastodynamic problems are shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

A general method for multiple crack problems in a finite plate

A novel method for the multiple crack problems in a finite plate is proposed in this paper. The basic stress functions of the solution consist of two parts. One is the Fredholm integral equation solution for the crack problem in an infinite plate, and the other is that of the weighted residual method for general plane problems. The combined stress functions are used in the analysis and the boundary conditions on the crack surfaces and the boundary are considered. After the coefficients of the functions have been determined, the stress intensity factors (SIF) at the crack tips can be calculated. Some numerical examples are given and it was observed that when the cracks are very short, the results compare very favorably with the existing results for an infinite plate. Furthermore, the influence of the boundary can be considered. This method can be used for arbitrary multiple crack problems in a finite plate.     

A hybrid BEM model

The hybrid stress method is very successful for stress concentration problems.^1–7 Especially for problems of fracture mechanics, procedures can be found that work efficiently for two- and three-dimensional problems. The rate of convergence with this method, evidently, is higher than that with conventional FE models. The BEM procedure, too, works more efficiently, but shows some essential disadvantages against the FEM, such as that for the direct method no symmetric positive definite matrix can be found and that there occur numerical problems at corners.^8,9 This happens also when BEM and FEM are even coupled commonly.^10–12. In the following, a hybrid BEM model will be described which combines the advantages of both the FEM and the BEM. It will be shown in this paper that BEM is very successful in formulating finite element functions for the hybrid assumed stress method.     

Hybrid and enhanced finite element methods for problems of soil consolidation

Hybrid and enhanced finite element methods with bi‐linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation. Both plane strain and axisymmetric problems are studied. It is found that by choosing appropriate interpolation of enhanced strains in the enhanced method, and by choosing appropriate interpolations of strains, effective stresses and enhanced strains in the hybrid method, the oscillations of nodal pore pressures can be eliminated. Several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented. It is also shown that for some situations, such as problems involving high Poisson's ratio and in other related problems where bending effects are evident, the performance of the enhanced and hybrid methods are superior to that of the conventional displacement‐based method. The results from the hybrid method are better than those from the enhanced method for some situations, such as problems in which soil permeability is variable or discontinuous within elements. Since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation, the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement‐based finite element method. The present enhanced method and hybrid method can be easily extended to non‐linear consolidation problems. Copyright © 2006 John Wiley & Sons, Ltd.     

Differential Constraint Scaling in Penalty Function Optimization

Penalty function optimization techniques are generally very successful in solving nonlinear programming problems. However, they can become computationally ineffective if certain of the constraints tend to dominate the entire constraint set. Under these circumstances, computational efficiency can often be restored by multiplying each constraint by an appropriate scale factor. This article presents a heuristic algorithm for computing such scale factors at periodic intervals during the computation. The method is applied to several sample problems, including some problems which are intentionally ill-scaled and others which are of a more realistic nature. The method is shown to be beneficial in all cases.