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研究生:朱茂玄
研究生(外文):Mau-ShiuanJu
論文名稱:開圓孔之非均質平板之應力集中
論文名稱(外文):Stress Concentration in Non-Homogeneous Plates with a Circular Hole
指導教授:譚建國譚建國引用關係
指導教授(外文):Jian-Guo Tan
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:2012
畢業學年度:100
語文別:中文
論文頁數:47
中文關鍵詞:應力集中狀態空間法傳遞矩陣
外文關鍵詞:stress concentrationstate space approachtransfer matrix
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本文採用狀態空間法解析非均質無窮板開洞之應力集中問題。在圓柱座標下,建立非均質無窮板開洞之狀態空間方程式。考慮彈性係數沿徑向為非均質情況下,以有系統的矩陣運算與推導,求得問題之解析解。對特殊非均質型式則採用傳遞矩陣方法,作數值解析。分析結果顯示:
1.彈性係數之漸弱趨勢越大,應力集中現象越顯著,且應力極值均產生於開孔周圍距其內徑五倍範圍內。
2.彈性係數變化趨勢越大,傳遞矩陣位移部份誤差亦較大。

On the basis of the state space approach, stress concentration problems around a hole in a radially inhomogeneous plate is analyzed. The state equations of a hole in a radially inhomogeneous plate is established in the cylindrical coordinates. The numerical analysis method is used through systematical calculation and matrix operation when Young's modulus is radially inhomogeneous. For a general radially inhomogeneous material, transfer matrix is used. Numerical results are presented to investigate the stress concentration around the circular notch. The conclusions show:

1.When Young's modulus's variation is getting smaller and this trend is getting bigger, Stress concentration phenomenon is more obvious, the extreme values of stress all occur in a five times inner diameter area around the hole.

2.When Young's modulus's variation is bigger, the error of displacement by transfer matrix is also bigger.

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
符號表 VII
第一章 緒論 1
1-1 研究動機 1
1-2 論文大綱 2
第二章 二維圓柱座標系統之基本方程式和傳統解析方法 3
2-1 基本方程式 3
2-2 傳統解析方法 4
2-3 開孔處固定之傳統解析方法 6
第三章 狀態空間之非均質開孔無窮板解法 8
3-1 狀態空間方程式 8
3-2 開孔處未受力 9
3-3 開孔處固定 12
第四章 狀態空間傳遞矩陣之解法 15
4-1 傳遞矩陣之圖形示意 15
4-2 傳遞矩陣之解法詳述 17
4-3 邊界條件 20
第五章 數值結果與探討 22
5-1 形式之分析結果 22
5-2 形式之分析結果 25
5-3 使用傳遞矩陣優劣性 27
第六章 結論 31
參考文獻 32
附錄A 33
附錄B 38
附錄C 43

1.Tarn,J.Q, Tseng,W.D.,Chang,H.H.,A circular elastic cylinder under its own weight.International Journal of Solid and Structures, 46,2886-2896,2009.
2.Tarn,J.Q,Tseng,W.D.,Chang,H.H.,A Hamiltonian State Space Approach for 3D Analysis of circular cantileves.Journal of Elasticity,101,207-237,2010
3.Tarn,J.Q,A state space formalism for anisotropic elasticity.Part I:Rectilinear anisotropic,39,5143-5155,2002
4.Tarn, J.Q., Chang, H.H., Tseng, W.D., Axisymmetric deformation of a transversely Isotropic cylindrical body: A Hamiltonian state-space approach. Journal of Elasticity 97,131-154,2009.
5.Tarn, J.Q., Tseng, W.D., Exact analysis of curved beams and arches with arbitrary end conditions: A Hamiltonian state space approach. Journal of Elasticity 107,39-63,2012.
6.Wang, Y.M., Tarn, J.Q., Hsu, C.K., State space approach for stress decay in laminates. International Journal of Solids and Structures 37,3535-3553
7.Mohsen Mohammadi,John R.Dryden,Liying Jiang,Stress concentration around a hole in a radially inhomogeneous plate,International Journal of Solid and Structures,48,483-491,2011.
8.Mohsen Mohammadi,John R.Dryden,Influence of the spatial variation Poisson's ratio upon the elastic field in nonhomogeneous axisymmetric bodies,International Journal of Solid and Structures,46,788-795,2009.
9.Tarn,J.Q,Wang Y.M,Laminated composite tubes under extension, torsion, bending, shearing and pressuring: a state space approach,International Journal of Solids and Structures 38, 9053-9075, 2001.
10.Tarn,J.Q,Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads,International Journal of Solids and Structures, 38, 8189--8206, 2001.
11.Tarn,J.Q, Chang,H.H.,Extension, Torsion, Bending, Pressuring and Shearing of Piezoelectric Circular Cylinders with Radial Inhomogeneity,Journal of Intelligent Material Systems and Structures, 16, 631--641, 2005.


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