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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 葉超雄 | |
dc.contributor.author | Chia-Jung Tsai | en |
dc.contributor.author | 蔡佳蓉 | zh_TW |
dc.date.accessioned | 2021-06-16T23:28:08Z | - |
dc.date.available | 2015-08-10 | |
dc.date.copyright | 2012-08-10 | |
dc.date.issued | 2012 | |
dc.date.submitted | 2012-07-31 | |
dc.identifier.citation | [1] Gauthier, R. D. (1982), “Experimental investigations on micropolar media,” in Mechanics of Micropolar Media, Edited by O. Brulin and R.K.T. Hsieh, World Scientific, pp. 395-463.
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[37] Iesan, D. and Scalia, A. (2003), “On complex potentials in the theory of microstretch elastic bodies,” Int. J. Engng. Sci., Vol. 41, pp. 1989-2003. [38] Iesan, D. and Nappa, L. (2006), “Method of complex potentials in linear microstretch elasticity,” Int. J. Engng. Sci., Vol. 44, pp. 797-806. [39] Kulesh, M. A., Matveenko, V. P. and Shardakov, I. N. (2003), “Parametric analysis of analytical solutions to one- and two-dimensional problems in couple-stress theory of elasticity,” Zeitschrift für Angewandte Math. Mech. (ZAMM) 83, No.4,pp.238-248. [40] Korepanov,V. V., M.A. Kulesh, V.P. Matveenko, and I.N. Shardakov (2007), “Analytical and numerical solutions for static and dynamic problems of the asymmetric theory of elasticity,” Physical Mesomechanics, Vol. 10, pp. 281-293. [41] Korepanov, V. V., Matveenko, V. P. and Shardakov, I. N. (2008), “Numerical study of two-dimensional problems of nonsymmetric elasticity,” Mechanics of Solids, Vol. 43, pp.218-224. [42] Liang, K. 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(2008), “Integral representation for the solution of a crack problem under stretching pressure in plane asymmetric elasticity,” in Integral Methods in Science and Engineering (2008): pp. 247-256 , January 01. 121 [52] Szeidl,Gy. and Dudra, J. (2011), “A birect boundary element formulation for the first plane problem in the dual system of micropolar elasticity,” Computational Methods in Applied Sciences, Vol. 24, pp.185-224. [53] Hadjesfandiari, A. R.,and Dargush, G. F. (2011), “Fundamental solutions for isotropic size-dependent couple stress elasticity,” Arxiv preprint arXiv:1107.2912, 2011 - arxiv.org [54] Hadjesfandiari, A. R., and Dargush, G. F. (2012), “Boundary element formulation for plane problems in couple stress elasticity,” International Journal for Numerical Methods in Engineering, Vol. 89, pp. 618-636. [55] Potapenko, S. (2002), “Application of the boundary integral equation method in the problem of torsion of micropolar bars,” Ph D. dissertation, University of Alberta, Edmonton, Canada. [56] Potapenko,S., Schiavone, P., and Mioduchowski, A. (2003), “On the solution of mixed problems in anti-plane micropolar elasticity,” Mathematics and Mechanics of Solids, Vol. 8, pp.151-160. [57] Potapenko, S. (2005), “Fundamental sequences of functions in the approximation of the solution to the mixed boundary-value problem in anti-plane Cosserat elasticity,” Acta Mechanica 177, pp. 61-69. [58] Potapenko, S. (2005), “A generalized Fourier approximation in anti-plane Cosserat elasticity,” Journal of Elasticity, Vol. 81, pp.159-177. [59] Potapenko,S., Schiavone, P., and Mioduchowski, A. (2006), “On the solution of the torsion problem in linear elasticity with microstructure,” Mathematics and Mechanics of Solids, Vol. 11, pp.181-195. [60] Potapenko, S. 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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65167 | - |
dc.description.abstract | 廣義聖維南問題是柱體不計徹體力與體力偶作用且側面無曳引力僅在端部承受彎曲、拉伸、扭轉與撓曲等外力作用,處理此方面之問題將有助於在聖維南材料靜力實驗中,藉由理論計算結果,與量測外力作用下之位移,進行比對量得材料參數,便於日後在相同材料下,使用此材料參數去分析及預測物體之力學行為。然而,在微小的物體時,因尺度效應,傳統連體力學無法有效地預測物體之受力行為,因此引入帶微結構的連體理論來分析,故要預測、分析微小物體之力學行為時,必須計算微結構柱體的聖維南問題,求得其在外力作用下之位移場。本文探討在材料均質、等向下,中心對稱與非中心對稱(手徵特性)之微極彈性柱體(具三個位移與三個微旋轉自由度)聖維南問題,重新推導並解釋其求解策略。在分析微極彈性材料之一般力學行為時,因微觀場耦合機制存在,使得其他外力形式問題也一併關聯進來,因此與傳統彈性力學不同之處在於進行分析、計算時,不能單純的只分析單一問題而是連其他問題也一併要納入考量!此處將針對實心圓柱及同心環形斷面微極彈性柱體之作為計算範例,分析外力作用下聖維南問題之位移場解析解。該解析解可以提供日後相似案例之數值分析作比較,以檢驗數值方法與分析結果之正確性(例如用BEM分析微極彈性偏心圓管柱體之扭轉問題時,須先比較驗證同心環形斷面柱體解析解之結果)。 | zh_TW |
dc.description.provenance | Made available in DSpace on 2021-06-16T23:28:08Z (GMT). No. of bitstreams: 1 ntu-101-R99521242-1.pdf: 1570124 bytes, checksum: e23cc15b316ca69b61293a187575d4dd (MD5) Previous issue date: 2012 | en |
dc.description.tableofcontents | 摘要 i
Abstract ii 目錄 iii 圖目錄 vi 符號表 vii 第 一 章 緒論 1 1.1 研究動機與目的 1 1.2 文獻回顧與微結構連體理論簡介 2 1.2.1 廣義聖維南問題之提出與其推廣至微結構連體理論 2 1.2.2 微結構連體理論模型 3 1.2.3 微極彈性體材料性質之分類(依組成律分類) 4 1.3 微極彈性理論之基本方程式 5 1.3.1 平衡方程式 6 1.3.2 幾何方程式 6 1.3.3 組成律 6 1.3.4 曳引力邊界條件 7 1.4 論文架構 7 第 二 章 均質等向且中心對稱微極彈性材料廣義聖維南問題之求解策略 9 2.1 基本定義與假設 10 2.2 廣義聖維南問題及半逆解法 11 2.3 彎曲、拉伸與扭轉 13 2.3.1 給定變形場之設定 13 2.3.2 共平面耦合場(ν3=φα=0) 14 2.3.3 反平面耦合場(να=φ3=0) 17 2.3.4 待定係數as(s=1,2,3,4)之求解 19 2.3.5 座標原點與斷面形心重合之情形 24 2.4 撓曲 25 2.4.1 給定變形場之設定 25 2.4.2 共平面耦合場(ν3'=φα'=0) 27 2.4.3 反平面耦合場(να'=φ3'=0) 27 2.4.4 待定係數bs、cs(s=1,2,3,4) 之求解 27 2.4.5 座標原點與斷面形心重合之情形 28 第 三 章 微極彈性材料圓柱斷面柱體之廣義聖維南問題 31 3.1 彎曲、拉伸與扭轉 33 3.1.1 廣義平面變形問題一 34 3.1.2 廣義平面變形問題二 46 3.1.3 廣義平面變形問題三 51 3.1.4 廣義平面變形問題四 54 3.1.5 關聯剛度計算與給定位移場待定係數之求解 59 3.2 撓曲 67 3.3 廣義聖維南問題之給定變形場總場一覽 75 3.3.1 彎曲、拉伸與扭轉問題之變形總場(Fα=0) 75 3.3.2 撓曲問題之變形總場(F3=Mi=0, F1=0, F2≠0) 79 第 四 章 具手徵特性微極彈性柱體廣義彎曲、拉伸與扭轉問題 81 4.1 廣義彎曲、拉伸與扭轉問題之求解策略 82 4.1.1 給定變形場之設定 82 4.1.2 廣義平面變形問題之平衡方程式與邊界條件 83 4.1.3 待定係數as(s=1,2,3,4)之求解 90 4.1.4 座標原點與斷面形心重合之情形 92 4.2 圓形與環形斷面柱體之廣義拉伸與扭轉問題求解 94 4.2.1 廣義平面變形問題三 96 4.2.2 廣義平面變形問題四 101 4.2.3 關聯剛度計算與給定位移場待定係數之求解 107 4.2.4 拉伸與扭轉問題給定變形總場一覽 109 第 五 章 結論與未來展望 112 5.1 結論 112 5.2 未來展望 114 參考文獻 116 | |
dc.language.iso | zh-TW | |
dc.title | 具手徵特性微極彈性材料之廣義聖維南問題 | zh_TW |
dc.title | Saint-Venant's Problem for Micropolar Elasticity with Chirality | en |
dc.type | Thesis | |
dc.date.schoolyear | 100-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳東陽,陳國慶,鄧崇任 | |
dc.subject.keyword | 廣義聖維南問題,手徵特性,微極彈性理論,實心圓形斷面柱體,同心環形斷面柱體, | zh_TW |
dc.subject.keyword | chiral effect,micropolar elastic theory,circular cylinder,circular cylinder with concentric hole, | en |
dc.relation.page | 123 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2012-07-31 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
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