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???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
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dc.contributor.advisor | 楊永斌(Yeong-Bin Yang) | |
dc.contributor.author | Min-Chung Cheng | en |
dc.contributor.author | 鄭閔中 | zh_TW |
dc.date.accessioned | 2021-06-13T02:28:27Z | - |
dc.date.available | 2012-08-09 | |
dc.date.copyright | 2011-08-09 | |
dc.date.issued | 2011 | |
dc.date.submitted | 2011-08-01 | |
dc.identifier.citation | Argyris, J. H., Dunne, P. C., Scharpf, D. W. (1978), “On large displacement-small strain
analysis of structures with rotational degrees of freedom”, Comput. Meth. Appl. Mech. Eng., 14(1978), 401-451. Argyris, J. H., Hilpert, G. A., Malejannakis, Scharpf, D. W. (1979a), “On the geometrical stiffness of a beam in space: A consistent v. w. approach”, Comput. Meth. Appl. Mech. Eng., 20(1979), 105-131. Argyris, J. H., Balmer, H., Doltsinis, J. St., Dunne, P. C., Haase, M., Kleiber, M., Malejannakis, G. A., Mlejnek, H. P., Muller, M., Scharpf, D. W. (1979b), “Finite element method: The natural approach”, Comput. Meth. Appl. Mech. Eng., 17/18(1979), 1-106 Argyris, J. H., Tenek, L., Mattsson A. (1998), “BEC: A 2-node converging shear deformable isotropic and composite beam element based on 6 rigid-body and 6 straining modes”, Comput. Meth. Appl. Mech. Eng., 152(1998), 281-336. Cook, R. D., Malkus, D. S., Plesha, M. E., Witt, R. J. (2001), “Concepts and Applications of Finite Element Analysis”, 2nd edn, John Wiley, New York, U.S.. Bathe K. J. (1996), “Finite Element Procedures”, Prentice-Hall. London, England. Bathe K. J., and Bolourchi, S. (1979), “Large displacement analysis of three- dimensional beam structures”, Int. J. Number. Meth. Eng., 14,961-986 Bergan, P. G. (1978), “Solution technique for nonlinear finite element problems”, Int. J. Number. Meth. Eng., 12, 1677-96. Fung, Y. C. (1965), “Foundations of Solid Mechanics”, Prentice Hall, Englewood Cliffs, N.J. Leu, L. J. and Yang, Y. B. (1990), “Effects of rigid body and stretching on nonlinear analysis of trusses”, J. Eng. Mech., ASCE, Vol. 116 (10), 2582-98. Mattiasson, K. (1981), “Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals”, Int. J. Number. Meth. Eng., Vol. 17(1), 145-153. Papadrakakis, M. (1981), “Post-buckling analysis of spatial structures by vector iteration method”, Comput. Struct., 14(5-6), 393-402. Poter, F. L. and Powell, G. H. (1971), “Static and dynamic analysis of inelastic frame structures”, Report, Earthquake Engineering Research Center, University of California, Berkeley, California, EERC, 71-73. Ramm, E. (1981), “Strategies for tracing the nonlinear response near limit point”, in Nonlinear Finite Element Analysis in Structural Mechanics, Wunderlich, W., Stein, E., and Bathe, K.-J. (eds), Springer-Verlag, Berlin, FRG, 63-89. Timoshenko, S. P. and Gere, J. M. (1961), “Theory of Elastic Stability”, McGraw-Hill, New York. Washizu, K. (1982), “Variational Methods in Elasticity and Plasticity”, 3rd ed., Pergamon press, Oxford, England. Williams, F. W. (1964), “An approach to the nonlinear behavior of the members of a rigid jointed plane framework with finite deflections”, Quart. J. Mech. Appl. Math., Vol. 17, 451-469. Yang, Y. B. and Chiou, H. T. (1987), “Rigid body motion test for nonlinear analysis with beam elements”, J. Eng. Mech., ASCE, Vol. 113 (9), 1404-1419. Yang, Y. B. and Kuo, S. R. (1992), “Frame buckling analysis with full consideration of joint compatibilities”, J. Eng. Mech., ASCE, Vol. 118 (5), 871-889. Yang, Y. B. and Kuo, S. R. (1994), “Theory and Analysis of Nonlinear Framed Structure”, Prentice-Hall, Singapore. Yang, Y. B. and Leu, L. J. (1991b), “Force recovery procedures in nonlinear analysis”, Comput. & Struct., Vol. 41(6), 1255-1261. Yang, Y. B., Lin, S. P., Leu, L. J. (2007a), “Solution strategy and rigid element for nonlinear analysis of elastically structures based on updated Lagrangian formulation”, J. Eng. Struct., 29(2007), 1189-1200. Yang, Y. B., Lin, S. P., Chen, C. S. (2007b), “Rigid body concept for geometric nonlinear analysis of 3D frames plates and shell based on the updated Lagrangian formulation”, Comput. Methods Appl. Mech. Engrg., 196(2007), 1178-1192 Yang, Y. B. and McGuire, W. (1985), “A work control method for geometrically nonlinear analysis”, in Proc. 1985 International Conference on Numerical Methods in Engineering: Theory and Application, Middleton, J., and Pande, G. N. (eds.), University College Swansea, Wales, U.K., 913-921. Yang, Y. B. and McGuire, W. (1986a), “Stiffness matrix for geometric nonlinear analysis”, J. Eng. Mech., ASCE, Vol. 112 (4), 857-877. Yang, Y. B. and Shieh, M. S. (1990), “Solution method for nonlinear problems with multiple critical points”, AIAA J., Vol. 28(12), 2110-2116 郭世榮 (民國八十年),'空間構架的靜力及動力穩定理論',國立台灣大學博士 論文。 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/31074 | - |
dc.description.abstract | 有關於結構的幾何非線性分析,文獻中一般利用元素的自然變形來求解元素內力,即對元素軸向位移進行修正,得到元素在變形過程時軸向的實際伸長量,此法於梁式結構的分析中可以得到很好的結果,但是對於其他自然變形於有限元素法中不易定義之結構型式,此法則較不容易應用;此外,在過去文獻中,也可以外在勁度矩陣的觀念將剛體運動效應排除,但是此一概念在計算上並不如自然變形法來得精確,也未被廣泛使用,因此,本研究的目的在於推導合理之外在勁度矩陣以改善此法,增加其可行性,使得此一概念在計算元素內力時能更加完善。在本研究中利用文獻中對於二維梁及三維梁所定義的各種變形模態,以及幾何勁度矩陣的性質,推導外在勁度矩陣,並針對三維梁元素於空間中旋轉所引致的彎矩效應作修正,以外在勁度矩陣概念建立內力校正式,在經由實例分析過後,可以驗證本研究所建立的內力校正式在分析非線性結構的可行性,並滿足幾何非線性分析的需求。 | zh_TW |
dc.description.abstract | A geometrically nonlinear analysis can be basically decomposed into two phases: the predictor phase and corrector phase. How to calculate the member forces for each incremental step in the corrector phase is a critical issue, as it controls the accuracy of the solution. In many previous works, the member forces are obtained by a well-known method based on the natural deformations. In calculating the natural deformations, the axial displacement of each element is modified as an approximation of the real axial extensions. This method is effective in the analysis of structures with beam elements, but it cannot be readily applied to other types of elements for which the natural deformations are difficult to define. On the other hand, in some previous studies, the concept of external stiffness matrix has also been used to eliminate the influence of rigid body motions in calculating the member forces. This concept has the advantage that the natural displacements need not be directly computed, but in comparison with the former method, it is not accurate enough, which may lead to slow convergence for some problems. Therefore, the objective of this thesis is to improve the external stiffness matrix method and to extend its practicability by deriving physically qualified external stiffness matrices.Based on various natural and rigid body modes presented previously for the two-dimensional and three-dimensional beams, along with the properties of the external stiffness matrix, this thesis will first derive qualified external stiffness matrices, which will then be modified through incorporation of the moments induced by the rotation of the beam in the three-dimensional space. Next, the formula for calculating the member forces incorporating the concept of external stiffness matrix will be derived. Finally, through the numerical verifications, it is demonstrated that the member force formula presented herein is feasible and can be generally used in the geometrically nonlinear analysis of structures. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T02:28:27Z (GMT). No. of bitstreams: 1 ntu-100-R98521202-1.pdf: 1550145 bytes, checksum: 6a01079afb36c56b83b34d175fe6dff3 (MD5) Previous issue date: 2011 | en |
dc.description.tableofcontents | 目錄
口試委員會審定書 I 致謝 II 英文摘要 III 中文摘要 V 第一章 導論 1 1.1 研究動機與目的 1 1.2 研究範圍 1 第二章 結構非線性增量分析理論 3 2.1 非線性推演法簡介 3 2.2 狀態說明 3 2.3 虛功方程式推導 4 2.4 更新式Lagrange推演法 6 2.5 增量平衡方程式之有限元素模型 8 2.6 剛體運動法則(Yang and Chiou, 1987) 9 2.7 元素內力之計算 11 2.7.1 自然變形法 11 2.7.2 外在勁度法 12 2.8 結論 13 第三章 外在幾何勁度矩陣推導 18 3.1 前言 18 3.2 桁架元素 18 3.2.1 桁架元素之增量勁度方程式 19 3.2.2 桁架元素之外在幾何勁度矩陣 20 3.3 二維梁元素 22 3.3.1 二維梁之增量勁度方程式 22 3.3.2 外在勁度矩陣推導 25 3.3.3 外在勁度矩陣之檢核 26 3.4 三維梁元素 28 3.4.1 三維梁之增量勁度方程式 29 3.4.2 外在勁度矩陣推導 34 3.3.3 外在勁度矩陣之檢核 37 3.3.4 引致彎矩矩陣之修正 43 3.5 結論 46 第四章 幾何非線性分析之數值方法 54 4.1 前言 54 4.2 數值方法比較 55 4.3 廣義位移控制法(Yang and Shieh, 1990) 56 4.4 非線性分析程序 59 4.5 結論 63 第五章 例題驗證 65 5.1 前言 65 5.2 桁架元素 66 5.3 二維梁元素 67 5.4 三維梁元素 70 5.4 結論 72 第六章 結論與未來展望 89 6.1 結論 89 6.2 未來展望 90 參考文獻 91 圖目錄 第二章 圖2.1 三維空間中之物體運動 15 圖2.2 受初始荷重之桿件 15 圖2.2 (a) 剛體旋轉前 15 圖2.2 (a) 剛體旋轉後 15 圖2.3 受力梁之剛體運動行為 16 圖2.3 (a) 剛體旋轉前 16 圖2.3 (a) 剛體旋轉後 16 圖2.4 剛體運動與自然變形比較 17 圖2.4 (a) 達到挫屈狀態之懸臂梁 17 圖2.4 (b) 達到挫屈狀態之門字型剛架 17 第三章 圖3.1 空間桁架元素之自由度 47 圖3.2 桁架元素之各種變形態 47 圖3.2(a) 桁架自然變形模態 47 圖3.2(b) 桁架x、y、z方向之剛體平移 47 圖3.2(c) 桁架xy、xz方向之剛體旋轉 48 圖3.3 受初始荷重之桁架元素 48 圖3.3 (a) C1狀態之初始力作用 48 圖3.3 (b) 經xy平面之剛體旋轉 48 圖3.3 (c) 經xz平面之剛體旋轉 49 圖3.4 平面梁元素之自由度 49 圖3.5 二維梁元素之各種變形模態 50 圖3.5 (a) 二維梁元素之自然變形模態 50 圖3.5 (b) 二維梁元素之剛體運動模態 50 圖3.6 三維梁於不同狀態之座標系 51 圖3.6 (a) C1狀態時三維梁之座標系 51 圖3.6 (b) C2狀態時三維梁之座標系 51 圖3.7 三維梁元素之各種變形模態 52 圖3.7 (a) 三維梁元素之自然變形模態 52 圖3.7 (b) 三維梁元素之剛體運動模態 53 第四章 圖4.1 非線性之荷載-位移曲線 64 圖4.2 GSP的正負號特性 64 第五章 圖5.1 雙桿件桁架(第一種載種狀況) 74 圖5.2 雙桿件桁架(第二種載種狀況) 74 圖5.3 24根桿件圓拱形桁架結構 75 圖5.4 受剪力作用之懸臂梁 75 圖5.5 受軸壓力作用之懸臂梁 75 圖5.6 受端點彎矩作用之懸臂梁 75 圖5.7 William構架 76 圖5.8 兩端為鉸接之扁平拱結構 76 圖5.9 兩端為鉸接之圓拱結構 76 圖5.10 三維懸臂梁結構之側向挫屈 77 圖5.11 受撓曲作用之角形三維梁構架 77 圖5.12 受撓曲作用之三維梁桿件 77 圖5.13 雙桿件桁架中央結點之荷載-位移曲線 78 圖5.14 雙桿件桁架中央結點之荷載-垂直位移曲線 78 圖5.15 雙桿件桁架中央結點之荷載-水平位移曲線 79 圖5.16 圓拱形桁架於結點2之荷載-水平位移曲線 79 圖5.17 圓拱形桁架於結點2之荷載-垂直位移曲線 80 圖5.18 受剪力作用之懸臂梁的荷載-位移曲線 80 圖5.19 受軸壓力作用之懸臂梁的荷載-位移曲線 81 圖5.20 受端點彎矩作用之懸臂梁的荷載-位移曲線 81 圖5.21 William構架中央結點之荷載-位移曲線 82 圖5.22 扁平拱結構於不對稱載重下之荷載-位移曲線 82 圖5.23 圓拱結構於不對稱載重下之荷載-位移曲線 83 圖5.24 圓拱結構於不對稱載重下之荷載-位移曲線 83 圖5.25 三維懸臂梁發生側向挫屈之荷載-位移曲線 84 圖5.26 角形三維梁構架: 與 之關係 84 圖5.27 角形三維梁構架: 與 之關係 85 圖5.28 受撓曲作用之三維梁桿件: 與 之關係 85 圖5.29 受撓曲作用之三維梁桿件: 與 之關係 86 表目錄 第五章 表5.1 受剪力作用之懸臂梁於不同校正子之總迭代次數比較表 87 表5.2 受軸壓力作用之懸臂梁於不同校正子之總迭代次數比較表 87 表5.3 受端點彎矩作用之懸臂梁於不同校正子之總迭代次數比較表 87 表5.4 William構架於不同校正子之總迭代次數比較表 87 表5.5 扁平拱結構於不同校正子之總迭代次數比較表 87 表5.6 圓拱結構於不同校正子之總迭代次數比較表 87 表5.7 發生側向挫屈之三維懸臂梁於不同校正子的總迭代次數比較表 88 表5.8 角形三維梁構架之極限彎矩值比較表 88 表5.9 角形三維梁構架於不同校正子之總迭代次數比較表 88 表5.10 受撓曲作用之三維梁桿件之極限彎矩值比較表 88 表5.11 受撓曲作用之三維梁桿件於不同校正子之總迭代次數比較表 88 | |
dc.language.iso | zh-TW | |
dc.title | 以合理的外在勁度矩陣進行結構幾何非線性分析 | zh_TW |
dc.title | Geometric Nonlinear Analysis of Structures with Qualified External Stiffness Matrix | en |
dc.type | Thesis | |
dc.date.schoolyear | 99-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 王寶璽,郭世榮,張凱淳 | |
dc.subject.keyword | 幾何非線性,j外在勁度矩陣,剛體運動,自然變形,內力校正式, | zh_TW |
dc.subject.keyword | geometrically nonlinear analysis,natural deformations,external stiffness matrix,rigid body motions,corrector, | en |
dc.relation.page | 93 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2011-08-01 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
Appears in Collections: | 土木工程學系 |
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