博碩士論文 953202006 詳細資訊




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姓名 莊凱迪(Kai-Ti Chuang)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 Blatz-Ko圓對稱波方程差分式的群分析
(Group analysis of the finite difference schemes for the Blatz-Ko spherical wave equation)
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摘要(中) 本論文主要研究Blatz-Ko材料圓形對稱動態波方程式,將非線性偏微分方程轉換至非線性常微分方程,使得求解過程簡化,再經由李群理論推導波方程各種的等值表示式與差分式,並利用Euler方法,Lax方法,Lax-Wendroff方法推導波方程各個差分式組合,各個差分式組合給予邊界條件,來觀察與分析最大誤差值,穩定特性,一致特性,準確特性。
摘要(英) This thesis investigates the symmetry properties of the finite difference schemes for the spherical wave equation for Blatz-Ko materials. We use the Euler method, Lax method and Lax-Wendroff method to derive difference schemes and investigate their group properties. The maximum error, stability, consistency and precision of these schemes are analyzed.
關鍵字(中) ★ Blatz-Ko材料
★ 圓對稱差分式
★ 波方程
★ 群的分析
關鍵字(英) ★ the finite difference schemes
★ Group analysis
★ Blatz-Ko spherical wave equation
論文目次 摘要 Ⅰ
英文摘要 II
誌謝 Ⅲ
目錄 Ⅳ
表目錄 Ⅵ
圖目錄 Ⅶ
第一章緒論 1
第二章 Blatz-Ko圓形波方程及其李群 3
第三章 Blatz-Ko圓形波方程等值表示式的李群 7
第四章 Blatz-Ko圓形波方程差分式的李群 10
4-1 Euler顯式差分式 11
4-2 Lax差分式 13
4-3 Lax-Wendroff差分式 14
第五章 Blatz-Ko圓形波方程差分式之數值分析 16
5-1 前言 16
5-2 Euler scheme 分析 18
5-2-1 Euler scheme (4.4)式之數值計算 18
5-2-2 Euler scheme (4.5)式之數值計算 21
5-3 Lax scheme 分析 24
5-3-1 Lax scheme (4.7)式之數值計算 24
5-3-2 Lax scheme (4.8)式之數值計算 27
5-4 Lax-Wendroff 分析 31
5-4-1 Lax-Wendroff (4.9)式之數值計算 31
5-4-2 Lax-Wendroff(4.11)式之數值計算 32
第六章結論 107
結論 109
參考文獻 108
參考文獻 1.F.A.McClintock, A criterion for ductile fracture by the growth of holes. J.Appl. Mech., 35, 363-371 (1968).
2.A.Needleman, Void growth in an elastic-plastic medium. J.Appl. Mech., 39, 964-970 (1972).
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, 2-15 (1977).
4.U.Stigh, Effects of interacting cavities on damage parameter. J.Appl. Mech, 53, 485-490 (1986).
5.A.N.Gent,Cavitation in rubber: a cautionary tale. Rubber Chem.Tech., 63, G49-G53 (1990).
6.H.S.Hou and R.Abeyarante, Cavitation in elastic and elastic-plastic solids, J.Mech.Phys.Solids, 40, 571-592 (1992).
7.C.O.Horgan and D.A.Polignone,Cavitation in nonlinearly elastic solids: a review.Appl.Mech.Rev., 48, 471-485 (1995).
8.J.M.Ball, Discontinous equilibrium solutions and cavitation in nonlinear elasticity. Phil.Trans.R.Soc.Lond, A306, 557-610 (1982).
9.C.A.Stuart, Radially symmetric cavitation for hyperelastic materials, Ann.Inst.Henri Poincare-Analyse non lineare, 2, 33-66 (1985).
10.C.O.Horgan and R.Abeyaratne, A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void. J.Elasticity, 16, 189-200 (1986).
11.F.Meynard, Existence and nonexistence results on the radially symmetric cavitation problem. Quart.Appl.Math. 50, 201-226 (1992).
12.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, 395-401 (1994).
13.S.Biwa, Critical stretch for formation of a cylindrical void in a compressible hyperelastic material. Int.J.Non-Linear Mech., 30, 899-914 (1995).
14.H.C.Lei(李顯智) and H.W.Chang, Void formation and growth in a class of compressible solids. J.Engrg.Math., 30, 693-706 (1996).
15.X.-C. Shang and C.-J. Cheng, Exact solution for cavitated bifurcation for compressible hyperelastic materials. Int.J.Engrg.Sci., 39, 1101-1117 (2001).
16.M.S.Chou-Wang and C.O.Horgan, Cavitation in nonlinear elastodynamics for neo-HooKean materials. Int.J.Engrg.Sci., 27, 967-973 (1989).
17.P.J. Blatz and W.L. Ko, Application of finite elastic theory to the deformation of rubbery materials. Trans.Soc. Rheol., 6, 223-251 (1962).
18.A. Mioduchowski and J.B. Haddow, Combined torsional and telescopic shear of a compressible hyperelastic tube. J. Appl. Mech., 46, 223-226. (1979)
19.M. Cheref, M. Zidi and C. Oddou, Analytical modelling of vascular prostheses mechanics. Intra and extracorporeal cardiovascular fluid dynamics. Comput. Mech. Pub, 1, 191-202 (1998).
20.M. Zidi, Finite torsional and anti-plane shear of a compressible hyperelastic and transversely isotropic tube. Int. J. Engrg. Sci, 38, 1481-1496 (2000).
21.L.V. Ovsiannikov, Group Analysis of Differential Equations (W. F. Ames, trans.). Academic Press, New York (1982).
22.N.H. Ibragimov, Tramsformation groups applied to mathematical physics. Reidel, Boston( 1985).
23.P.J. Olver, Applications of Lie Groups to Differential Equations. Springer-Verlag, New York (1986).
24.G.W. Bluman and S. Kumei , Symmetries and Differential Equations. Springer-Verlag , New York (1989).
25.S. Maeda, Canonical structure and symmetries for discrete systems. Math. Japan, 25, 405-420 (1980).
26.Ju. I. Sokin, The Method of Differential Approximation. Spring-Verlag, New York (1983).
27.S. Maeda, The similarity method for difference equations. J. Inst. Math. Appl, 38, 129-134 (1987).
28.V.A. Dorodnitsyn, Transformation groups in a space of difference variables. J. Sov. Math., 55, 1490-1517 (1991).
29.W.F. Ames, F.V. Postell and E. Adams, Optimal numerical algorithsm. Appl.. Numer. Math, 10, 235-259 (1992).
30.V.A. Dorodnitsyn, and P. Winternitz, Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations. Nonlinear Dyn, 22, 49-59 (2000).
31.H.K. Hong and C.S. Liu, Lorentz group SO(5,1) for perfect elastoplasticity with large deformation and a consistency numerical scheme. Int. J. Nonlinear Mech. 34, 1113-1130 (1999).
32.V.A. Dorodnitsyn, R. Kozlov, and P. Winternitz, Lie group classification of second order ordinary differential equations. J. Math. Phys., 41, 480-504 (2000).
33.V.A. Dorodnitsyn, and R. Kozlov, Heat transfer with a source: the complete set of invariant difference schemes. J. Nonliner Math. Phys., 10, 16-50 (2003).
34.D. Levi, S. Tempesta and P. Winternitz, Umbral calculus, difference equations and the discrete Schrodinger equation. J. Math. Phys., 45, 4077-4015 (2004).
35.F. Valiquette and P. Winternitz, Discretization of partial differential equations preserving their physical symmetries. J. Phys. A:Math. Gen., 38, 9765-9783 (2005).
36.C.S. Liu and Y.L. Ku, A combination of group preserving scheme and Runge-Kutta method for the intergration of Landau-Lifshitz equation. CMES-Computer Modeling Engrg. Sci., 9, 151-177 (2005).
37.A. Bourlioux, C. Cyr-Gagnon and P. Winternitz, Difference schemes with point symmetries and their numerical tests. J. Phys. A: Math. Gen., 39, 6877-6896 (2006).
38.C.S. Liu, An efficient backward group preserving scheme for the backward in time Burgers equation. CMES-Computer Modeling Engrg. Sci., 12, 55-65 (2006).
39.H.C.Lei(李顯智), Journal of the Chinese Institude of Engineers, Vol. 30, 557-567 (2007).
指導教授 李顯智(Hsien-Chih Lei) 審核日期 2008-7-22
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