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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 吳光鐘(Kuang-Chong Wu) | |
| dc.contributor.author | Tsungyen Tsai | en |
| dc.contributor.author | 蔡宗諺 | zh_TW |
| dc.date.accessioned | 2021-06-16T02:26:38Z | - |
| dc.date.available | 2020-08-10 | |
| dc.date.copyright | 2015-08-10 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-08-04 | |
| dc.identifier.citation | [1] A. Hrennikoff, Solution of Problems of Elasticity by the Frame-Work Method, Journal of Applied Mechanics, Vol. 8, A619–A715, 1941.
[2] R. Courant, Variational Methods for the Solution of Problems of Equilibrium and Vibrations, Bulletin of the American Mathematical Society 49: 1–23, 1943. [3] I. Fredholm, Sur une classe d'équations fonctionnelles, Acta Mathematica, Vol. 27 pp. 365-390, 1903. [4] G. Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, Nottingham, England: T. Wheelhouse, 1828. [5] F. J. Rizzo, An Integral Equation Approach to Boundary Value Problems of Classical Elastostatics. Quart. Appl. Math, Vol. 25, pp.83-95, 1967. [6] P. K. Banerjee and R. Butterfiled, Boundary Element Methods in Geomechanics, Chapter 16 in: Finite Element in Geomechanics, Ed. G. Gudehs, John Wiley, Chichester, UK; Proc. NMSRM, University of Karlsruhe, FRG, 1975. [7] G. Bezine, Boundary Integral Formulation for Plate Flexure with Arbitrary Boundary Conditions, Mechanics Research Communications, Vol. 5, p. 197, 1978. [8] M. Stern, A General Boundary Integral Formulation for the Numerical Solution of Plate Bending Problems, International Journal of Solids and Structures, Vol. 15, p. 769, 1979. [9] G. Shi and G. Bezine, A General Boundary Integral Formulation for the Anisotropic Plate Bending Problems, Journal of Composite Materials, Vol. 22, pp. 694-716, 1988. [10] C. Hwu, Boundary Integral Equations for General Laminated Plates with Coupled Stretching–Bending Deformation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 466, pp. 1027-1054, 2010. [11] K. C. Wu, Y. T. Chiu and Z. H. Hwu, A New Boundary Integral Equation Formulation for Linear Elastic Solids, Journal of Applied Mechanics, Vol. 59, pp. 344-348, 1992. [12] C. Hwu, Stroh-like Formalism for the Coupled Stretching-Bending Analysis of Composite, International Journal of Solids and Structures, Vol. 40, pp. 3681-3705, 2003. [13] C. Hwu, Anisotropic Elastic Plate, Springer, New York, 2010. [14] K. C. Wu and P. S. Hsiao, A New Boundary Integral Formulation for Bending of Anisotropic Plates, Acta Mechanica, accepted, 2015. [15] C. Hwu, and M. C. Hsieh Extended Stroh-like Formalism for Electro-Elastic Composite Laminates and Its Applications to Hole Problems. Smart Materials and Structures, Vol. 14, pp. 56-68, 2005. [16] Z. Q. Cheng and J. N. Reddy, Octet Formalism for Kirchhoff Anisotropic Plates, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol.458, p. 1499, 2002. [17] C. B. Prasad and M. J. Shuart, Moment Distributions Around Holes in Symmetric Composite Laminates Subjected to Bending Moments, AIAA Journal, Vol.28, pp. 877-882, 1990. [18] G. Bezine, On A Method of Comparison for Plate Elements in Finite Element Engineering Software Programs, Mechanics Research Communications, Vol. 29, pp. 35-43, 2002. [19] C. Hwu, Some Explicit Expressions of Stroh-like Formalism for Coupled Stretching–Bending Analysis. International Journal of Solids and Structures, Vol. 47, pp. 526-536, 2010. [20] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, New York, McGraw-hill, 1959. [21] S. G. Lekhnitskii, Anisotropic Plate, Gordon and Breach, London, 1968. [22] T.C.T. Ting, Anisotropic Elasticity: Theory and Applications. New York/Oxford: Oxford University Press, 1996. [23] J. N. Goodier, V. The Influence of Circular and Elliptical Holes on the Transverse Flexure of Elastic Plates, Philosophical Magazine Series 7, Vol. 22, pp. 69-80, 1936. [24] E. J. Barbero, Finite Element Analysis of Composite Material using AbaqusTM, CRC Press, 2013. [25] Z. Q. Cheng and J. N. Reddy, Laminated Anisotropic Thin Plates with an Elliptic Inhomogeneity. Mechanics of Material, Vol. 37, pp. 647-657, 2004. [26] K. C. Wu. and P. S. Hsiao, An Exact Solution for an Anisotropic Plate with An Elliptic Hole under Arbitrary Remote Uniform Moments, Composites Part B: Engineering, Vol. 75, pp. 281-287, 2015. [27] ABAQUS, ABAQUS Analysis User's Manual Version 6.10.1, Dassault Systèmes Simulia Corp., Providence, RI, USA, 2011. [28] T. C. T. Ting, A Modified Lekhnitskii Formalism à la Stroh for Anisotropic Elasticity and Classifications of the Matrix N, Proceedings of the Royal Society of London, A455, pp. 69-89, 1999. [29] 蕭培需, 一個用於分析異向彈性彎曲問題的新邊界積分法, 國立臺灣大學應用力學研究所碩士論文, 2014. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/53630 | - |
| dc.description.abstract | 本文使用一個新的邊界積分方程式分析含雙孔洞的異向彈性平板承受遠端彎曲或扭轉力矩之應力集中的問題。該邊界積分方程式是以柯西積分式配合古典版理論與異向彈性力學問題之Stroh方法而得。除運用此邊界積分方程式外，另亦使用有限元素分析軟體ABAQUS，計算孔壁之曲率與力矩。兩種方法比較之結果顯示出以位移為基礎的有限元素求得的力矩有較大的誤差，而邊界元素法則可以直接求得力矩，因此準確度較高；但對位移而言，邊界元素法之誤差與有限元素軟體相去不遠。 | zh_TW |
| dc.description.abstract | This work uses a new boundary integral equation (BIE) and finite element method (FEM) to analyze an infinite anisotropic plate containing two elliptic/circular holes subjected to remote bending or twisting moments. The foundation of the boundary integral equation is the classical plate theory with Cauchy integral formula. The BIE is used to calculate the curvatures and moments on the boundaries directly. Numerical examples are given for orthotropic and isotropic plates with circular or elliptic holes under uniform bending and twisting moments. Comparison of the numerical results with the analytic solution for one hole shows that in general BIE can achieve higher accuracies in evaluating moments while BIEs and FEM have comparable accuracies for computing deflections. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T02:26:38Z (GMT). No. of bitstreams: 1 ntu-104-R02543003-1.pdf: 3535242 bytes, checksum: 1da956748115a1fb045b7c9044974c83 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
誌謝 ii 摘要 iii ABSTRACT iv 目錄 v 圖目錄 vii 表目錄 xi 第1章 導論 1 1.1 文獻回顧與研究動機 1 1.2 本文大綱 2 第2章 古典板理論與Stroh-Like理論 3 2.1 古典板理論 3 2.1.1 基本假設 3 2.1.2 位移場假設 3 2.1.3 應變與位移關係 3 2.1.4 彈性組成律 4 2.1.5 靜力平衡方程式 6 2.1.6 統御方程式 7 2.2 Stroh-Like 理論 7 第3章 解析解 11 3.1 橢圓孔上的旋轉角與曲率 11 3.2 計算待定常數0 15 3.3 橢圓孔上之力矩 17 3.4 橢圓孔上之位移 19 第4章 數值分析方法 20 4.1 邊界積分方程式 20 4.2 以邊界積分方程式之數值求解孔洞問題 22 4.3 利用座標轉換求解孔洞邊界上之力矩 25 4.4 利用曲率之數值結果計算轉角與位移 28 4.5 ABAQUS求解流程 29 第5章 含單孔洞彈性板計算結果 32 5.1 含單圓孔之等向性與正交性平板 32 5.1.1 含單圓孔之無限板施加M11 33 5.1.2 含單圓孔之無限板施加M12 42 5.2 含單橢圓孔之等向性與正交性平板 50 5.2.1 含單橢圓孔之無限板施加M11 50 5.2.2 含單橢圓孔之無限板施加M12 57 第6章 含雙圓孔彈性板計算結果 64 6.1 等向性與正交性平板於遠端施加M22 64 6.1.1 等向性材料 65 6.1.2 正交性材料 74 6.2 含雙圓孔之等向性與正交性平板於遠端施加M11 83 6.2.1 等向性材料 84 6.2.2 正交性材料 91 6.3 孔緣彎矩隨兩圓孔中心距改變之影響 99 6.4 含圓孔與橢圓孔之等向性平板於遠端施加M11 101 第7章 結論與未來展望 104 7.1 結論 104 7.2 未來展望 105 參考文獻 106 附錄一 109 | |
| dc.language.iso | zh-TW | |
| dc.subject | 解析解 | zh_TW |
| dc.subject | 有限元素法 | zh_TW |
| dc.subject | 邊界積分法 | zh_TW |
| dc.subject | 異向彈性板 | zh_TW |
| dc.subject | 孔洞 | zh_TW |
| dc.subject | 應力集中 | zh_TW |
| dc.subject | 無限板 | zh_TW |
| dc.subject | 史磋法 | zh_TW |
| dc.subject | analytical solutions | en |
| dc.subject | anisotropic elastic plates | en |
| dc.subject | boundary integral equation | en |
| dc.subject | finite element method | en |
| dc.subject | Stroh-like formalism | en |
| dc.subject | elliptical hole | en |
| dc.subject | stress concentrations | en |
| dc.subject | infinite plate | en |
| dc.title | 以邊界元素法分析含 雙橢圓孔洞異向性彈板受彎矩作用之應力集中現象 | zh_TW |
| dc.title | BEM Analysis for Stress Concentrations of Bending Problem of Anisotropic Plates Containing Two Elliptical Holes | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張正憲(Jeng-Shian Chang),陳正宗,陳俊杉,陳世豪 | |
| dc.subject.keyword | 異向彈性板,邊界積分法,有限元素法,史磋法,孔洞,應力集中,無限板,解析解, | zh_TW |
| dc.subject.keyword | anisotropic elastic plates,boundary integral equation,finite element method,Stroh-like formalism,elliptical hole,stress concentrations,infinite plate,analytical solutions, | en |
| dc.relation.page | 110 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2015-08-05 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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|---|---|---|---|
| ntu-104-1.pdf 未授權公開取用 | 3.45 MB | Adobe PDF |
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