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研究生:吳聲展
研究生(外文):Sheng-Jhan Wu
論文名稱:數值解析不同形狀內含物之中性扭轉
論文名稱(外文):Difficient shapes of neutral coated inhomogeneity
指導教授:陳東陽陳東陽引用關係
指導教授(外文):Tung-yang Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:85
中文關鍵詞:扭轉剛度中性
外文關鍵詞:torsional rigidityneutral
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本文主要目的是用數值解析不同形狀內含物之圓柱中性扭轉問題。所謂中性扭轉為當內含物置入基材後,不使基材之翹曲函數改變者,稱之為中性扭轉。本文中之內含物主要分成中空內含物與異質內含物兩種,異質內含物即中空內含物原中空之部分填入另一種材料。
The present paper is concerned with exact solutions in the Saint-Venant torsion of circle composite bars.We show the existence of a large class of thickly coated inhomogeneities which leave the vanishing warping function in the circle bas undisturbed. These are called "partially neutral"inhomogeneities. If the tossional rigidity of the host bar is unchanged as well, they are called"completely neutral".
摘要………………………………………………………………………….Ⅰ
誌謝……………………………………………………………………….…Ⅱ
目錄………………………………………………………………………….Ⅲ
圖目錄…………………………………………………………………….…Ⅴ
第一章 緒論………………………………………………………………...1
1.1 理論背景與文獻回顧………………………………………………...1
1.2 論文內容簡介………………………………………………………...2
第二章 任意形狀之部分中性中空內含物………………………………...4
2.1 部份中性中空內含物之精確解……………………………………..4
2.2 滿足精確解的一些實例……………………………………………..8
2.3 部份中性之共焦點中空橢圓………………………………………16
第三章 任意形狀之部分中性異質內含物……………………………….36
3.1 部份中性異質內含物之精確解……………………………………36
3.2 滿足精確解的一些實例……………………………………………39
3.3 部份中性之共焦點異質橢圓………………………………………42
第四章 完全中性內含物有關扭轉剛度之探討………………………….64
4.1 將扭轉剛度用映射函數與翹曲函數的係數表示…………………64
4.2 完全中性之圓形異質內含物………………………………………67
4.3 完全中性之共焦點異質橢圓………………………………………69
4.4 完全中性之epitrochoidal 異質內含物……………………………71
第五章 結果與討論……………………………………………………….78
參考文獻…………………………………………………………………….80
附錄A……………………………………………………………………….83
自述…………………………………………………….……………………85
1. Grabovsky, Y., Milton G. W., & Sage, D.S. 2000 Exact relation for effective tensors of composites:necessary condition and sufficient condition. Commun. Pure and Apple. Math., Vol. LⅢ, 330-353.

2. Chen, T., Benvensite, Y. & Chuang, P. C. 2001 Exact solution in torsion of composite bars:thickly coated neutral inhomogeneities and composite cylinder assemblages. Submitted for publication.

3. Chen, T. & Huang, Y. L. 1998 Saint-Venant torsion of two-phase circumferentially symmetric compound bar. J. Elasticity.53, 109-124.

4. Chen, T. 2001 Torsion of a rectangular checkerboard and the analogy between rectangular and curvilinear cross-sections. Quart. J. Mech. Appl. Math. 54,227-241.

5. Booker, J. R. and Kitipornchai, S. (1971) Torsion of multilayered rectangular section. J. Engng Mech. 97, 1451-1468.

6. Benvensite, Y. & Chen, T. 2001 On the Saint-Venant torsion of composite bars with imperfect interfaces. Proc. R. Soc. Lond. A457, 231-255.

7. Benvensite, Y. & Milton, T. 1999 Neutral inhomogeneities in conduction. Phenomena. J. Mech. Phys. Solids 47, 1873-1892.

8. Timoshenko, S. P. and Goodier, J. N. (1970) Theory of Elasticity. McGraw-Hill, New York.

9. Sokolnikoff, I. S. 1956 Mathematical Theory of Elasticity. McGraw-Hill, New York.

10. Hashin, Z. & Rosen, B. W. 1964 The elastic moduli of Fiber-reforced materials J. Appl. Mech. 31, 223-232.

11. Lipton, R. 1998 Optimal fiber configurations for maximum torsional rigidity. Arch. Ration Mech. Anal. 144, 79-106.

12. Milton, G. W. & Serkov, S. K. 2001 Neutral coated inclusion in conductivity and anti-plane elasticity. Proc. R. Soc. Lond. A, in press.

13. Muskhenlishvili, N. I. 1953 Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen.

14. Ru, C. Q. 1998 Interface design of neutral elastic inclusion. Int. J. Solids Struct. 35, 559-572.
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