基于边界积分法的V型切口应力分析与病态矩阵影响

发布时间：2018-04-20 04:34

本文选题：应力 + 边界积分　；参考：《天津职业技术师范大学》2017年硕士论文

【摘要】：本课题研究起始于圆棒料切口尖端应力应变场的分析,其目的是为裂纹技术做理论上的铺垫,而裂纹技术是原甘肃工业大学魏庆同教授发现的。例如,在制造高速钢刀具时,应用裂纹技术下料,比用锯进行割断效率提高很多。圆棒料切口尖端应力应变场,是一个三维的弹塑性问题,求解析解非常困难,一般人们都用有限元法进行数值求解,可以说求解切口尖端应力应变场的主要方法是有限元法。但有限元法也有一定局限,例如,在应力集中附近区域需要划分比较密集的网格,使得未知量的数目和总体刚度矩阵的带宽变得很大,从而给求解带来困难。另外用有限元分析时,往往由位移近似值来计算应力,所得边界应力结果一般较差,而应力集中又正好发生在边界上。本论文采用边界积分数值方法求解应力应变场,是相对于有限元方法的变革尝试,尤其在计算手段获得改进的情况下,是一种有益的探索。该方法较早文献起源于1973年W.Rzasnicki所写的俄亥俄特雷多大学(Univ Toledo Ohio)的一篇博士论文,其后戴怡于1995年进行了相应研究,并编写FORTRAN进行计算。需要说明的是,用边界积分数值方法求解应力应变场会遇到病态矩阵问题,病态矩阵在许多工程问题都会遇到,例如在北斗卫星定位系统和逆向工程求解过程中都会遇到,所以该课题研究不仅对裂纹技术有重要意义,也对相关共性基础理论研究有重要意义。本论文在以上研究基础上,对原问题涉及的弹塑性参数重新进行了核对、校正,并改进计算手段,应用MATLAB语言进行相应计算,进一步展现了该问题的病态矩阵特性,研究了相应的解决办法,改进了计算结果,使得应用边界积分数值方法求解应力应变场获得进展。
[Abstract]:This subject begins with the analysis of stress and strain field at the tip of round bar notches. The purpose of this study is to lay a theoretical foundation for the crack technique, which was discovered by Professor Wei Qingtong of Gansu University of Technology. For example, in the manufacture of high-speed steel cutting tools, the cutting efficiency of using crack cutting technology is much higher than that of cutting with saw. The stress and strain field at the tip of round bar notch is a three dimensional elastoplastic problem. It is very difficult to solve the analytical solution. Generally, people use finite element method to solve the stress and strain field at the notch tip. It can be said that the main method to solve the stress and strain field at the notch tip is the finite element method. But the finite element method also has some limitations, for example, the area near the stress concentration needs to be divided into more dense meshes, which makes the number of unknown variables and the bandwidth of the total stiffness matrix become very large, which makes it difficult to solve the problem. In addition, when the finite element analysis is used, the stress is usually calculated by the approximate value of the displacement. The result of the boundary stress is generally poor, and the stress concentration just happens on the boundary. In this paper, the boundary integral numerical method is used to solve the stress-strain field, which is a reform attempt compared with the finite element method, especially in the case of improved calculation means, it is a useful exploration. The method originated from a doctoral thesis written by W.Rzasnicki in 1973 by Univ Toledo Ohio.After that, Dai studied it in 1995 and compiled FORTRAN to calculate it. It should be pointed out that the problem of ill-conditioned matrix will be encountered in solving the stress-strain field with boundary integral numerical method, and the ill-conditioned matrix will be encountered in many engineering problems, such as Beidou satellite positioning system and reverse engineering. Therefore, the research of this subject is not only of great significance to crack technology, but also to the research of relevant general basic theory. On the basis of the above research, the elastoplastic parameters involved in the original problem are checked and corrected again, and the calculation method is improved, and the corresponding calculation is carried out by using MATLAB language, which further shows the ill-conditioned matrix characteristics of the problem. The corresponding solutions are studied and the calculation results are improved. The boundary integral numerical method is used to solve the stress-strain field.
【学位授予单位】：天津职业技术师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O346.1

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