关于伴随矩阵的讨论

本文讨论了ｎ阶方阵Ａ的伴随阵Ａ的性质，给出了严格的证明。     

逆矩阵的求法

可逆矩阵及逆矩阵在矩阵的理论和应用中都占有很重要的地位,本文给出了逆矩阵的几种常见的求法。     

求逆矩阵的几种方法

矩阵是线性代数中的主要研究对象与研究工具,而逆矩阵是矩阵理论中的一个非常重要的概念,如何判断一个矩阵是否可逆以及如何求矩阵的逆矩阵就显得非常重要。求逆矩阵方法很多,本文归纳了如下几种:定义法;利用伴随矩阵求逆法;利用伴随矩阵求逆法的推论求逆;利用逆矩阵的性质求逆法;利用矩阵的初等变换求逆;分块对角阵求逆法。     

亚正定矩阵的若干性质

亚正定矩阵是正定矩阵概念的推广 .利用正规矩阵和乘积可交换矩阵的重要性质 ,给出了亚正定矩阵的三个充分条件以及其合同矩阵的两个分解形式 .     

K-对角占优矩阵的性质

介绍了K-对角占优矩阵的概念,给出了K-对角占优矩阵的若干性质。     

基于矩阵求逆理论的曲梁单元刚度矩阵解析解

基于矩阵求逆理论,提出矩阵求逆的综合法。弹性核法求解曲梁单元的刚度矩阵时,由于柔度矩阵的每个元素表达式繁琐,难以直接求逆得到曲梁单元的刚度矩阵。既有相关文献均指出采用数值方法求逆可得出曲梁单元的刚度矩阵。应用矩阵求逆的综合法,推导出曲梁单元刚度矩阵的解析解,并通过算例分析比较,证明了公式的正确性。由此,在编制曲梁杆系梁段有限元的计算程序时,解析解的应用不但简化了程序的编写,而且节约了计算机工作单元,提高了计算精度。     

部分逆M矩阵完备问题的研究

采用图论的方法对任意阶非负部分矩阵,讨论了其是否有逆M矩阵完备式的问题.提出反特征矩阵的概念.在非负部分矩阵的特征矩阵对应的模型图无法分析时,考虑其反特征矩阵对应的模型图,由此得到它的逆M完备式.重点讨论了部分矩阵的反特征矩阵对应的图为块团图的情况下如何得到它的逆M完备式.     

对称矩阵的性质及应用

本文讨论了实对称矩阵的若干性质以及它们的应用。     

生成分支q-矩阵的Feller性质

研究了生成分支q-矩阵,得到了该矩阵Feller性的充要条件。     

只用列变换求非异阵的逆阵

在线性代数中，若矩阵A的行列式的值不为0，则该矩阵为非异阵，非异阵有逆矩阵，逆矩阵是唯一的，用伴随矩阵的方法求逆矩阵计算量大而繁琐，所以可以用矩阵的初等变换求逆矩阵，本文给出用列变换求非异阵的逆阵。     

Development of a fast fluid dynamics-based adjoint method for the inverse design of indoor environments

The computational fluid dynamics (CFD)-based adjoint method may be appropriate for the inverse design of indoor environments, considering both accuracy and efficiency, but a single design still requires tens of hours with the use of a personal computer. To speed up the inverse design process, this study evaluated four fast fluid dynamics (FFD) models in terms of solving the Navier–Stokes equations, integration with turbulence models, and solving the adjoint equations. This study implemented the FFD solvers in OpenFOAM and validated them for predicting steady-state and transient indoor airflow. This study then validated the FFD solvers for solving the adjoint equations and the FFD-based adjoint method for inverse identification problems and inverse designs in indoor environments. The results showed that FFD was 20 times faster than CFD in predicting transient indoor airflow, and similar computational accuracy could be maintained; the FFD-based adjoint method was 4–16 times faster than the CFD-based adjoint method in the inverse design process.     

Optimization of air supply location,size, and parameters in enclosed environments using a computational fluid dynamics-based adjoint method

Optimal design of an indoor environment based on specific design objectives requires a determination of thermo-fluid control methods. The control methods include the air supply location, size, and parameters. This study used a computational fluid dynamics- (CFD) based adjoint method to identify the optimal air supply location, size, and parameters. Through defining the air distribution in a certain area (design domain) as a design objective in a two-dimensional, ventilated cavity, the adjoint method can identify the air supply location, size, and parameters. However, the air supply location, size, and parameters were not unique, which implied multiple solutions. By using any of the air supply location, size, and parameters identified as boundary conditions for forward CFD simulations, the computed air distribution in the design domain was the same as that used as a design objective. Thus, the computing costs did not depend on the number of design variables.     

Inverse design of indoor environment using an adjoint RNG k‐ε turbulence model

The adjoint method can determine design variables of an indoor environment according to the optimal design objective, such as minimal predicted mean vote (PMV) for thermal comfort. The method calculates the gradient of the objective function over the design variables so that the objective function can be minimized along the fastest direction using an optimization algorithm. Since the objective function is controlled by the Reynolds‐averaged Navier‐Stokes (RANS) equations with the RNG k‐ε model during the optimization process, all the corresponding adjoint equations should be solved, rather than the “frozen turbulence” assumption used in previous studies. This investigation developed adjoint equations for the RNG k‐ε turbulence model and applied it to a two‐dimensional ventilated cavity and a three‐dimensional, two‐person office. Design processes with the adjoint RNG k‐ε turbulence model led to a near‐zero design function for the two cases, while those with the “frozen turbulence” assumption did not. This investigation has successfully used the new method to design a two‐person office with optimal thermal comfort level around the two occupants.     

基体组分优化对纤维水泥基复合材料应变硬化性能的影响

纤维增强复合材料(FRCC)在负荷下具有应变硬化和多裂缝类型特征,然而,并不是所有水泥基材料中加入一定量纤维就可得到应变硬化性能,基体组分,加工制作过程的不同和基体缺陷的差异影响着应变硬化的稳定性。依据取得应变硬化行为的微观力学模型和其他一些研究方法,探讨了水灰比、骨料、矿物掺合料、基体缺陷等因素变化对FRCC应变硬化能力的影响。结果表明:在微观力学模型的指导下,优化基体材料的组分能够稳定的取得应变硬化的行为。     

Inverse design of the thermal environment in an airplane cockpit using the adjoint method with the momentum method

Currently, the thermal environment in airplane cockpits is unsatisfactory and pilots often complain about a strong draft sensation in the cockpit. It is caused by the unreasonable air supply diffusers design. One of the best approaches to design a better cockpit environment is the adjoint method. The method can simultaneously and efficiently identify the number, size, location, and shape of air supply inlets, and the air supply parameters. However, the real air diffuser needed to design often have grilles, especially in the airplane cockpit, and the current method can only design the inlet as an opening. This study combined the adjoint method with the momentum method to directly identify the optimal air supply diffusers with grilles to create optimal thermal environment in an airplane cockpit (1) under ideal conditions and (2) with realistic constraints. Under the ideal conditions, the resulting design provides an optimal thermal environment for the cockpit, but it might not be feasible in practice. The design with realistic constraints provides acceptable thermal comfort in the cockpit, but it is not optimal. Thus, there is an engineering trade-off between design feasibility and optimization. All in all, the adjoint method with the momentum method can be effectively used to identify real air supply diffusers.     

Future directions for matrix organizations in Brazil

Although it is generally agreed that organizations should be designed and managed in an established manner, there is now an increasing trend towards a more informal approach characterized by greater flexibility. Factors such as rising educational levels and increasing rates of change in technological and social factors have encouraged the development of such organizational trends-one of the most important of which is the matrix organization. Although the matrix organization is not necessarily appropriate in all cases, it is believed that it is not merely a short-term fad, but a permanent and significant organizational innovation. The future role and development of the matrix organization is analysed, with particular consideration of the situation in Brazil. Future trends in critical issues are identified and discussed.     

Element stiffness matrix and modified coefficients for circular tube with tapered ends

By axially connecting a constant-section circular tube to two tapered circular tubes, a so-called circular tube with tapered ends structural member is obtained. To get the element stiffness matrix of a tube with tapered ends, a transfer matrix method is introduced in this paper. Transfer matrices for the constant-section tube and tapered tubes are derived firstly, and then the element stiffness matrix for a tube with tapered ends is obtained on the basis of the relationship of the transfer matrices. Two typical examples are given to verify the element stiffness matrix. And the stiffness matrix for a tube with tapered ends can be treated as a modification of the stiffness matrix for a constant-section tube. Stiffness modified coefficients are introduced to represent the modification, and a table of stiffness modified coefficients for tubes of frequently used dimensions is given at the end of the paper.     

关于沥青玛脂碎石混合料试验方法的探究

采用旋转压实方法进行上面层沥青玛脂碎石混合料配合比的研究,通过一系列试验,选择并确定了合适的旋转压实的试验参数,为今后沥青路面施工提供了科学数据。     

双锥型圆钢管的单元刚度矩阵及修正系数

本文采用传递矩阵法推导了双锥型圆钢管单元的空间弹性刚度矩阵。首先简略阐述了传递矩阵法的基本原理,推导了等截面圆钢管和锥型圆钢管的传递矩阵;然后利用传递矩阵关系原理推导出双锥型圆钢管单元的空间弹性刚度矩阵,并运用实例进行公式验证与误差分析,结果表明本文所推导的刚度矩阵具有足够精度,可用于工程分析,也可用于有限元程序的编制;最后在单元刚度矩阵的基础上提出了双锥型圆钢管的刚度修正系数,当进行稳定计算时,可将双锥型圆钢管等效成等截面圆钢管分析。文末给出常用双锥型圆钢管的刚度修正系数表,以供广大设计人员参考。