本文選題：應(yīng)力 + 邊界積分　； 參考：《天津職業(yè)技術(shù)師范大學(xué)》2017年碩士論文

【摘要】：本課題研究起始于圓棒料切口尖端應(yīng)力應(yīng)變場(chǎng)的分析,其目的是為裂紋技術(shù)做理論上的鋪墊,而裂紋技術(shù)是原甘肅工業(yè)大學(xué)魏慶同教授發(fā)現(xiàn)的。例如,在制造高速鋼刀具時(shí),應(yīng)用裂紋技術(shù)下料,比用鋸進(jìn)行割斷效率提高很多。圓棒料切口尖端應(yīng)力應(yīng)變場(chǎng),是一個(gè)三維的彈塑性問(wèn)題,求解析解非常困難,一般人們都用有限元法進(jìn)行數(shù)值求解,可以說(shuō)求解切口尖端應(yīng)力應(yīng)變場(chǎng)的主要方法是有限元法。但有限元法也有一定局限,例如,在應(yīng)力集中附近區(qū)域需要?jiǎng)澐直容^密集的網(wǎng)格,使得未知量的數(shù)目和總體剛度矩陣的帶寬變得很大,從而給求解帶來(lái)困難。另外用有限元分析時(shí),往往由位移近似值來(lái)計(jì)算應(yīng)力,所得邊界應(yīng)力結(jié)果一般較差,而應(yīng)力集中又正好發(fā)生在邊界上。本論文采用邊界積分?jǐn)?shù)值方法求解應(yīng)力應(yīng)變場(chǎng),是相對(duì)于有限元方法的變革嘗試,尤其在計(jì)算手段獲得改進(jìn)的情況下,是一種有益的探索。該方法較早文獻(xiàn)起源于1973年W.Rzasnicki所寫(xiě)的俄亥俄特雷多大學(xué)(Univ Toledo Ohio)的一篇博士論文,其后戴怡于1995年進(jìn)行了相應(yīng)研究,并編寫(xiě)FORTRAN進(jìn)行計(jì)算。需要說(shuō)明的是,用邊界積分?jǐn)?shù)值方法求解應(yīng)力應(yīng)變場(chǎng)會(huì)遇到病態(tài)矩陣問(wèn)題,病態(tài)矩陣在許多工程問(wèn)題都會(huì)遇到,例如在北斗衛(wèi)星定位系統(tǒng)和逆向工程求解過(guò)程中都會(huì)遇到,所以該課題研究不僅對(duì)裂紋技術(shù)有重要意義,也對(duì)相關(guān)共性基礎(chǔ)理論研究有重要意義。本論文在以上研究基礎(chǔ)上,對(duì)原問(wèn)題涉及的彈塑性參數(shù)重新進(jìn)行了核對(duì)、校正,并改進(jìn)計(jì)算手段,應(yīng)用MATLAB語(yǔ)言進(jìn)行相應(yīng)計(jì)算,進(jìn)一步展現(xiàn)了該問(wèn)題的病態(tài)矩陣特性,研究了相應(yīng)的解決辦法,改進(jìn)了計(jì)算結(jié)果,使得應(yīng)用邊界積分?jǐn)?shù)值方法求解應(yīng)力應(yīng)變場(chǎng)獲得進(jìn)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.
【學(xué)位授予單位】：天津職業(yè)技術(shù)師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O346.1

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