非線性彈性圓孔運動方程的李群分析

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：21

、訪客IP：18.226.181.246

姓名

徐茂豐(mao-feng xu) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

非線性彈性圓孔運動方程的李群分析

相關論文

★ 各種載重作用下neo-Hookean材料微孔動態分析	★ 劉氏保群算法於高雷諾數Burgers方程之應用及探討
★ 彈性材料圓孔非對稱變形近似解研究	★ HAF描述含圓孔橡膠材料三軸壓縮變形的誤差分析
★ 國立中央大學-HAF描述圓形微孔非對稱變形的誤差計算	★ 多微孔橡膠材料受拉變形平面應力分析
★ 非線性彈性固體微孔變形特性	★ 鋼絲網加勁高韌性纖維混凝土於RC梁構件剪力補強研究
★ 高韌性纖維混凝土(ECC)之材料配比及添加物對收縮及力學性質影響	★ 材料組成比例對超高性能纖維混凝土之工作性與力學性質之影響
★ 搜尋週期為四年時使用SDICAE作強震預測的最佳精度設定	★ 牛頓型疊代法二次項效應
★ GEH理論壓密量速算式	★ 擴散管流量解析解
★ 宏觀收斂迭代法速度比較	★ 二次項效應混合型牛頓疊代法之研究

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

本文主旨在研究非線性可壓縮彈性固體承受動態荷重時圓孔的擴張。成果有助於材料損壞機制的了解，也可促進非線性可壓縮彈性固體動態問題的了解。本研究所用的數學方法有一部分是最近才提出，相關的應用不多，本研究則可促進這方面的探尋。

摘要(英)

This project studies the dynamic expansion of a radially deformed circular cavity in a compressible nonlinear elastic solid. The result we shall obtain will facilitate the understanding of the mechanism of damage of materials. This study will also help us to capture the nature of dynamic deformations in compressible nonlinear elastic solids. Another goal of this project is to explore the abilities of some methods proposed recently for solving nonlinear partial differential equations.

關鍵字(中)

★ 材料損壞
★ 非線性彈性固體
★ 彈性動態問題

關鍵字(英)

★ elastodynamics
★ nonlinear elasticity
★ material damage

論文目次

目錄
頁次
摘要……………………………………………………… Ⅰ
英文摘要………………………………………………… Ⅱ
目錄……………………………………………………… Ⅲ
第一章緒論…………………………………………….. 1
1–1背景與動機....................................... 1
1–2 文獻回顧........................................ 2
1–3 論文內容........................................ 3
第二章基礎理論……………………………………….. 4
2–1 問題描述........................................ 4
2-1-1 圓柱體徑向變形................................. 4
2-1-2 圓球體徑向變形................................. 6
2–2 李群理論簡介.................................... 8
2-2-1微分方程的李群.................................. 9
2-2-2不變解.......................................... 10
第三章非線性偏微分方程的群與解............... 12
3–1前言............................................ 12
3–2微分方程之李群.................................. 13
3–3對稱群........................................... 34
3–4不變解........................................... 40
第四章群與解的探討…………………………………. 46
4–1對稱群的比較.................................... 46
4–2 微分方程的比例群................................ 47
第五章結論與建議……………………………………. 69
5–1 結論............................................ 69
5–2 建議............................................ 69
參考文獻………………………………………………… 71
附錄……………………………………………………… 73
附錄A............................................... 73
附錄A-1............................................. 75
附錄B............................................... 77
附錄B-1............................................. 79
附錄C............................................... 82
附錄C-1............................................. 85
附錄D............................................... 87
附錄D-1............................................. 90
附錄E............................................... 92
附錄E-1............................................. 95
附錄F............................................... 97
附錄F-1............................................. 100
表............................................ 102

參考文獻

參考文獻
1.F.A.McClintock, A criterion for ductile fracture by the growth of holes. J.Appl. Mech., 35 (1968) 363-371.
2.A.Needleman, Void growth in an elastic-plastic medium. J.Appl. Mech., 39 (1972) 964-970.
3.A.L.Gurson, Continuum theory of ductile rupture by void nucleation and growth : Part Ⅰ- yield criteria and flow rules for porous ductile media. J.Energ.Matl.Tech.,Trans.ASME, (1977) 2-15.
4.U.Stigh, Effects of interacting cavities on damage parameter. J.Appl. Mech, 53 (1986) 485-490.
5.H.S.Hou and R.Abeyarante, Cavitation in elastic and elastic-plastic solids, J.Mech.Phys.Solids, 40 (1992) 571-592.
6.A.N.Gent,Cavitation in rubber: a cautionary tale. Rubber Chem.Tech., 63 (1990) G49-G53.
7.C.O.Horgan and D.A.Polignone,Cavitation in nonlinearly elastic solids: a review. Appl.Mech.Rev., 48 (1995) 471-485.
8.H.C.Lei(李顯智) and H.W.Chang, Void formation and growth in a class of compressible solids. J.Engrg.Math., 30 (1996) 693-706.
9.J.M.Ball, Discontinous equilibrium solutions and cavitation in nonlinear elasticity. Phil.Trans.R.Soc.Lond, A306 (1982) 557-610.
10.C.A.Stuart, Radially symmetric cavitation for hyperelastic materials, Ann.Inst.Henri Poincare-Analyse non lineare, 2 (1985) 33-66.
11.C.O.Horgan and R.Abeyaratne, A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void. J.Elasticity, 16 (1986) 189-200.
12.F.Meynard, Existence and nonexistence results on the radially symmetric cavitation problem. Quart.Appl.Math. 50 (1992) 201-226.
13.S.Biwa, Critical stretch for formation of a cylindrical void in a compressible hyperelastic material. Int.J.Non-Linear Mech., 30 (1995) 899-914.
14.S.Biwa, E.Matsumoto and T.Shibata, Effect of constitutive parameters on formation of a spherical void in a compressible non-linear elastic material. J.Appl.Mech. 61 (1994) 395-401.
15.X.-C. Shang and C.-J. Cheng, Exact solution for cavitated bifurcation for compressible hyperelastic materials. Int.J.Engrg.Sci., 39 (2001) 1101-1117.
16.M.S.Chou-Wang and C.O.Horgan, Cavitation in nonlinear elastodynamics for neo-HooKean materials. Int.J.Engrg.Sci., 27 (1989) 967-973.
17.M. Cheref, M. Zidi and C. Oddou, Analytical modelling of vascular prostheses mechanics. Intra and extracorporeal cardiovascular fluid dynamics. Comput. Mech. Pub., 1 (1998) 191-202.
18.M. Zidi, Finite torsional and anti-plane shear of a compressible hyperelastic and transversely isotropic tube. Int. J. Engrg. Sci., 38 (2000) 1481-1496.
19.N. Roussos and D.P. Mason, On non-linear radial oscillations of an incompressible , hyperbolic spherical shell. Math. Mech. Solids, 7(2002)67-85.
20.R.Abeyaratne and C.O.Horgan, Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinear elastic medium. J. Elasticity, 15 (1985) 243-256.
21.J.K. Knowles and E. Sternberg, On the ellipticity of non-linear elastostatics for a special material. J. Elasticity, 5 (1975) 341-361.
22.C.O. Horgan, Remarks on ellipticity for the generalized Blatz-Ko constitutive model for compressible nonlinearly elastic solid. J. Elasticity, 42 (1996) 165-176.
23.A. Mioduchowski and J.B. Haddow, Combined torsional and telescopic shear of a compressible hyperelastic tube. J. Appl. Mech., 46 (1979) 223-226.
24.M. Zidi, Circular shearing and torsion of a compressible hyperelastic and prestressed tube. Int. J. Non-Linear Mech., 35 (2000) 201-209.
25.M. Zidi, Torsion and axial shearing of a compressible hyperelastic tube. Mech. Res. Comm., 26 (1999) 245-252.
26.李顯智,唐又新,孔洞承受的極限壓力,中華民國力學學會期刊,33(1997)205-
212.
27.P.J. Blatz and W.L. Ko , Application of finite elastic theory to the deformation of rubbery materials . Trans.Soc. Rheol. , 6 (1962) 223-251 .
28.Peter E. Hydon. Symmetry Methods For Differential Equations : a beginner's guide. Cambridge University Press, New York (2000)
29.W. Bluman and J.D. Cole, Similarity Method for Differential Equation. Springer-verlag, New York (1974)
30.Lawrence E. Malvern, Introduction To The Mechanics of a Continuous Medium. Prentice-Hall,Inc. Englewood Cliffs, N. J.

指導教授

李顯智(H.C.Lei)

審核日期

2003-7-8

推文