# 臺灣博碩士論文加值系統

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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 IAbstract II致謝 III目錄 IV圖目錄 VI符號表 VII第一章 緒論 11-1 研究動機 11-2 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 32-1 基本方程式 32-2 傳統解析方法 42-3 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 83-1 狀態空間方程式 83-2 開孔處未受力 93-3 開孔處固定 12第四章 狀態空間傳遞矩陣之解法 154-1 傳遞矩陣之圖形示意 154-2 傳遞矩陣之解法詳述 174-3 邊界條件 20第五章 數值結果與探討 225-1 形式之分析結果 225-2 形式之分析結果 255-3 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,101,207-237,20103.Tarn,J.Q,A state space formalism for anisotropic elasticity.Part I:Rectilinear anisotropic,39,5143-5155,20024.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 37,3535-35537.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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