臺灣博碩士論文加值系統

摘要
從第一個初始負載到極限負載，一細長的圓形工件其靜不定結構在彈塑性分析時會產生一系列的連續的塑性鉸，而裂縫的位置也會強烈地影響塑性鉸發展的順序，以及影響裂縫自我本身的穩定性。
圓形環受到對稱集中力作用的時候，使用基礎的彈性分析疊代法求得裂縫在穩定情形下塑性鉸的呈現，當環中形成四個塑性鉸的時候，圓形環將會發生崩潰(參考文獻【9】)。本文主要的目的，為利用數值計算來驗證文獻中的數值解，即經由二維邊界元素法分析一彈-塑圓形環，當圓形環中含有裂縫時，裂縫的位置會直接影響圓形環內連續塑性鉸的形成以及裂縫的穩定性。

Abstract

From the first initial load to limit load, a long and thin its quiet indefinite structure of round work piece will produce a series of continuous plasticity to cut with scissors while playing plasticity to analyse, and the position of the crack will influence plasticity to cut with scissors the order of development strongly, and influence the self- one's own stability of crack.
Round ring when affecting by symmetrical attention, use basic elasticity analyse pile take the place of law try to get crack whom plasticity cut with scissors appear under stabilizing situation, when form four pieces of plasticity to cut with scissors in the ring, the round ring will collapse (the list of references [9]) . The main purpose of this text, calculate to prove in order to utilize number value the number value in documents is solved, namely - mould the round ring via a ball of element law analysis of two-dimentional border, when containing the crack in the round ring, the position of the crack will influence the stabilities of forming and crack that continuous plasticity cuts with scissors in round ring directly.

目錄
第一章 緒論-----------------------------------------------------------------------1
1-1前言-------------------------------------------------------------------1
1-2文獻回顧-------------------------------------------------------------2
1-3理論介紹-------------------------------------------------------------2
第二章 原理-----------------------------------------------------------------------6
2-1基礎方程式----------------------------------------------------------6
2-2基礎解----------------------------------------------------------------6
2-3邊界積分方程式---------------------------------------------------10
2-4邊界條件------------------------------------------------------------12
2-5數值應用------------------------------------------------------------15
2-6矩陣表示------------------------------------------------------------16
第三章 裂縫圓形環的討論---------------------------------------------------18
3-1研究介紹-----------------------------------------------------------18
3-2建立模型-----------------------------------------------------------19
3-3邊界條件-----------------------------------------------------------23
3-4結果分析-----------------------------------------------------------29
3-4.0計算結果---------------------------------------------------29
3-4.1第一塑性鉸------------------------------------------------31
3-4.2第二塑性鉸------------------------------------------------38
3-4.3第三塑性鉸------------------------------------------------44
第四章 結論---------------------------------------------------------------------50
參考文獻--------------------------------------------------------------------------52
附錄--------------------------------------------------------------------------------54

參考文獻

【1】G. Fichera, “Linear Elliptic Equations of Higher Order in Two Independent Variables and Singular Integral Equations with Applications to Anisotropic Inhomogeneous Elasticity, Proceedings of Symposium on Partial Differential Equations and Continuous Mechanics”, University of Wisconsin Press, pp. 55-80, 1961.

【2】V.D. Kupradze, “Potential Mechods in the Theory of Elasticity”, Israel, Program of Scientific Translations, Jerusalem, 1965.

【3】F.J. Rizzo, “An Integral Equation Approach to Boundary Value Problems of Classical Elastostatics’’, Journal of Applied Mathematics, 25,pp.83-95,1967

【4】T.A. Cruse, “Numerical Solutions in Three Dimensional Elastostatics”, Journal of Solids and Structures, 5,pp. 1259-1274, 1969.

【5】C.A.Brebbia,J.C.F Telles and L.C. Wrobel,“Boundary Element Techniqes”,Springer-Verlag,New York,1970.

【6】G. Hsiao and W.L. Wendland, “A Finite Element Method for Some Integral Equations of the First Kind”, Journal of Mathematical Analysis Applications, 58, pp. 449-481, 1977.

【7】A. Ghobanpoor and J Zang, “Boundary Elemant Analysis of Crack Growth for Mixed Mode Center Slant Crack Problems”, Engineering Fracture Mechanics, Vol. 36, No.5 pp. 661-668, 1990.

【8】Lih-Jier Young,“A Boundary Element Of Fracture Surface Interence For Mixed Mode Loading Problems With Elastic Or Plastic Crack Tips”1994.



【9】Lih-Jier Young,“Plastic Hinges Development And Crack Stability Analysis In A Circular Ring”,International Journal Of Solids And Structures,2001

【10】邊界元素法－理論與工程應用良宜圖書有限公司，陳正宗，1990

【11】邊界元素法在圓形環上的運用，甘仁德，2002

【12】邊界元素法在具有鋸齒裂縫下四點彎矩工件上的應用，陳珈汶，2005

【13】邊界元素法對圓形環穩定性分析，王世源，2007

【14】邊界元素法在圓形環具有鋸齒裂縫下的應用，方伯睿，2007