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研究生： 徐茂豐
mao-feng xu
論文名稱： 非線性彈性圓孔運動方程的李群分析
指導教授： 李顯智
H.C.Lei
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
畢業學年度： 91
語文別： 中文
論文頁數： 107
中文關鍵詞： 材料損壞 、非線性彈性固體 、彈性動態問題
外文關鍵詞： elastodynamics, nonlinear elasticity, material damage
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    • 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。

    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.

    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

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