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研究生:紀志昌
研究生(外文):Chih-Chang Chi
論文名稱:剛體運動法則與增量力平衡在板殼結構幾何非線性理論分析之應用
論文名稱(外文):Geometric Nonlinear Theory of the Plates and Shells Structures Considering Rigid Body Rule and Incremental Force Equilibrium
指導教授:郭世榮郭世榮引用關係葉為忠
指導教授(外文):Shyh-Rong KuoWeichung Yeih
學位類別:博士
校院名稱:國立臺灣海洋大學
系所名稱:河海工程學系
學門:工程學門
學類:河海工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:200
中文關鍵詞:剛體運動法則增量力平衡幾何非線性板殼結構
外文關鍵詞:Rigid Body RuleIncremental Force EquilibriumGeometric NonlinearPlates and Shells
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剛體運動法則及力平衡是力學分析中必須滿足的兩個最基本條件,平板幾何非線性理論的增量虛功方程式、控制方程式、邊界條件及幾何勁度矩陣等,皆要滿足此二項基本的力學原理。本文的研究是在探討剛體運動法則及增量力平衡在板殼結構幾何非線性理論的應用,其研究內容可分成三個部分:第一是以更新式拉格蘭治描述法為基礎,利用虛功原理推導平板結構增量虛功方程式。其過程中,考慮六項非線性應變造成的非線性虛應變能,且完整推導變形後2C狀態平板邊界曳引力因旋轉變形產生彎矩引量所做的虛功,此虛功量在現有的文獻上未曾討論。由此求得的平板結構的幾何非線性增量虛功方程式,可正確通過剛體運動法則及增量力平衡檢測。第二是提出平板結構幾何非線性虛應變能的簡易推導方法,以避免傳統採用虛功法之繁雜且不易理解的推導過程。此簡易方法首先是建立增量虛功方程式滿足剛體運動及增量力平衡的條件方程式,接著應用此二組方程式,進行簡單的積分運算,求得幾何非線性虛應變能。此虛應變能將自動滿足剛體運動法則及增量力平衡二項基本力學條件。第三是建立平板元素幾何勁度矩陣滿足剛體運動及增量力平衡的條件方程式,並藉由此二條件方程式,提出一簡易的推導方法建立三角形平板元素外在幾何勁度矩陣。此推導過程僅需進行簡單的矩陣運算,可避免有限元素法冗長繁瑣的推導過程,而建立之元素幾何勁度矩陣僅與節點座標、節點力及節點彎矩等物理量有關,為一簡明的顯式表示型式,且在不同的直角座標系統下,皆保有相同固定的型式。應用此勁度矩陣進行幾何非線性分析時,將不需計算平板元素的內力,並且可直接以整體座標系統的物理量表示。此外,此幾何勁度矩陣在組合成結構勁度矩陣時,其反對稱項將相互抵銷,因此結構結構勁度矩陣仍保有對稱性質。
The rigid body rule and the force and moment equilibrium are basically two fundamental conditions for analysis of mechanics; therefore, the geometric nonlinear incremental virtual work equation, governing equation, boundary conditions and the geometric stiffness matrix of the plate structure should obey the basic two conditions. In this dissertation, applications of the rigid body rule and the incremental force and moment equilibrium with the geometric nonlinear theorem on the plate and shell structure are presented and main concerns are presented in three parts: the first, based on the update Lagrange formulation method, the incremental virtual work equation can be derived by using the virtual principle. In the deriving process, by considering the six terms of the nonlinear virtual strain energy arising from the virtual strains, the virtual work, produced from the incremental bending moment owing to the rotation of the plate after the deformed 2C state, can be reached and such virtual work has never been proposed in the literature. It should be noted that the derived geometric nonlinear incremental virtual work equation can fully pass both the rigid body rule and the force and moment equilibrium conditions; the second, a simple derivation for the nonlinear virtual strain energy is firstly proposed such that it can avoid the tedious derivation when the conventional virtual work method is adopted. The proposed simple method firstly constructs the incremental virtual work equation, which satisfies the rigid body rule and incremental force and moment equilibrium conditions and then, the geometric nonlinear virtual strain energy can be determined by simple integral calculation; the third and the last, the condition equation, for which the geometric stiffness matrix of the plate element satisfies the rigid body rule and the incremental force equilibrium conditions, is constructed and thus, a simple method for deriving the external geometric stiffness matrix of a reliable three-node triangular plate element is presented. It should be noted that this simple derivation method only needs some simple matrix operations and can avoid the tedious deriving process as compared with the finite element method. This geometric stiffness matrix of the element only relates with the nodal coordinates, nodal force and moment and actually is a simple explicit formulation. By adopting the stiffness matrix to conduct the geometric nonlinear analysis, the internal force of the plate element is not necessary to calculate and can further be presented in the global coordinate system. Besides, the skew-symmetric parts of the derived geometric stiffness matrix can be canceled out once they are merged into the global stiffness matrix of the structure. In this regard, this structural stiffness matrix becomes a symmetric one and thus, enhances its effectiveness.
目錄
第一章 導論 1
1.1 前言 1
1.2 文獻回顧與研究動機 1
1.3 研究目的與內容 6

第二章 剛體運動與增量力平衡之基本原理 9
2.1 導論 9
2.2 增量虛功方程式 11
2.2.1 虛功原理 11
2.2.2 Lagrangian 推演法之增量虛功方程式 14
2.3 剛體運動法則 17
2.3.1 剛體運動法則 18
2.3.2 幾何勁度矩陣之剛體運動檢測 19
2.3.3 增量虛功方程式之剛體運動檢測 21
2.4 增量力平衡方程式 23
2.4.1 增量力平衡方程式 24
2.4.2 幾何勁度矩陣之增量力平衡檢測 25
2.4.3 增量虛功方程式之增量力平衡檢測 28
2.5 剛體運動與增量力平衡之應用 31

第三章 平板結構穩定理論之探討 53
3.1 導論 53
3.2 平板結構的變形狀態的描述 55
3.2.1 1C狀態平板物理量之描述 56
3.2.2 2C狀態平板物理量之描述 59
3.3 平板之幾何非線性增量虛功方程式 63
3.3.1 線性虛應變能與非線性虛應變能 63
3.3.2 1C狀態及2C狀態邊界曳引力所作的虛功 65
3.3.3 平板幾何非線性理論之控制方程式及邊界條件68
3.4 小結 70

第四章 平板結構穩定理論之剛體運動及力平衡檢測 77
4.1 導論 77
4.2 平板穩定理論之剛體運動檢測 78
4.2.1 平板結構的剛體運動 78
4.2.2 增量虛功方程式的剛體運動檢測 80
4.3 平板穩定理論之增量力平衡檢測 83
4.3.1 平板結構的增量力平衡方程式 83
4.3.2 增量虛功方程式之增量力平衡檢測 86
4.4 小結 89

第五章 平板殼結非線性虛應變能之簡易推導 93
5.1 導論 93
5.2 剛體運動法則與增量力平衡 94
5.2.1 剛體位移之增量虛應變能 -應用剛體運動法則95
5.2.2 剛體虛位移之增量虛應變能 -應用增量力平衡99
5.3 平板幾何非線性虛應變能 103
5.3.1 幾何非線性增量虛應變能之簡易推導邏輯 103
5.3.2 面內作用力之非線性虛應變能 106
5.3.3 離開平面作用力之平板幾何非線性虛應變能 110
5.3.4 平板幾何非線性虛應變能 112
5.4 小結 113

第六章 簡易平板元素幾何勁度矩陣 119
6.1 導論 119
6.2 三角形平板元素定義(TPE) 120
6.3 平板元素滿足剛體運動法則之條件方程式 122
6.4 平板元素滿足增量力平衡之條件方程式 124
6.5 平板元素外在幾何勁度矩陣之推導 128
6.5.1 反對稱的幾何勁度矩陣 129
6.5.2 對稱的結構幾何勁度矩陣 131
6.6 小結 136

第七章 實例分析 139
7.1 數值範例 140
7.2 小結 148

第八章 結論與建議 175
8.1 結論 175
8.2 展望 177

參考文獻 179
附錄A1 185
附錄A2 187
附錄B 189
附錄C 191
附錄D 195
Argyris, J. H., Dunne, P. C., Malejannakis, G. A., Schelkle E.,(1977), "A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problems," Computer Methods in Applied Mechanics and Engineering, Vol. 10, pp. 371-403.
Argyris, J. H.,Hilpert, O., Malejannakis, G.A., and Scharpf, D. W.,(1979). "On the geometrical stiffness of a beam in space-a consistent a V.W.approach, "Comp. Mech. Eng, Vol. 20, pp. 105-131.
Argyris, J. H., Tenek, L., Olofsson, L.,(1997), "TRIC: a simple but sophisticated 3-node triangular element based on 6 rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells," Computer Methods in Applied Mechanics and Engineering, Vol. 145, pp. 11-85.
Bathe, K. J., Bolourchi, S.,(1979), "A geometric and material nonlinear plate and shell element," Computes & Structures, Vol. 11, pp.23-48.
Bathe, K. J., Bolourchi, S.,(1979), "Large displacement analysis of three-dimensional beam structures," International Journal for Numerical Methods in Engineering, Vol. 14, pp. 961-986.
Bathe, K. J.,(1982).Finite element procedutes in engineering analysis. Prentice-Hall, Inc., New York.
Batoz, J. L., Bathe, K. J., Ho, L. W.,(1980), "A study of three-node triangular plate bending element," International Journal for Numerical Methods in Engineering, Vol. 15, pp. 1771-1812.
Bosela, P. A., Ludwiczak, D. R.,(1996), "A new pre-loaded membrane geometric stiffness matrix with full rigid body capabilities," Computers and Structures, Vol. 60, No. 1, pp. 159-168.
Chajes, A.,(1974).Principles of structural stability theory. Englewood Cliffs, N.J., Prentice-Hall Book Co.,
Chen, W. and Cheung, Y. K.,(1998), "Refined triangular discrete kirchhoff plate element for thin plate bending, Vibration and buckling analysis," International Jornal for Numerical Methods in Engineering, Vol. 41,No.8, pp. 1507-1525.
Cheung, Y. K., Zhang, Y. X., Wanji, C.,(2000), "The application of a refilled non-conforming quadrilateral plate bending element in thin plate vibration and stability analysis," Finite Elements in Analysis and Design, Vol. 34, No. 2, pp. 175-191.
Cook, R. D.,(1987), "A plane hybrid element with rotational D.O.F, and adiustable stiffness," Int. J. Numer. Meth. Eng., Vol. 24, pp. 1499-1508.
Cook, R. D., Malkus, D. S., Plesha, M. E.,(1989), Concepts and applications of finite element analysis, third edition, John Wiley & Sons, New York.
Drawshi, D. and Betten, J.,(1992), "Axially symmetric deformations and stability of a geometrically nonlinear circular plate subjected to multiparametrical ststic loading," Archive of Applied Mechanics Vol. 62 pp. 455-462
Dumir, P. C. and Shingal, L.,(1986), "Nonlinear analysis of thick circular plates," J. Engrg. Mech., ASCE, Vol. 112 , No.3 ,pp. 260-272
Ferreira, A. J. M., Barbosa, J. T.,(2000), "Buckling behaviour of composite shells," Composite Structures, Vol. 50, pp. 93-98.
Gallagher, R. H., Padlog, J.,(1963), "Discrete element approach to structural instability analysis," AIAA journal. Vol. 1,No.6, pp. 1437-1439.
Guo, M. W., Harik, I. E., Ren, W. X.,(2002), "Buckling behavior of stiffened laminated plates," International Journal of Solids and Structures, Vol. 39, No. 11, pp. 3039-3055.
Hodges, D. H., Atilgan, A. R., and Danielson, D. A.,(1993), "A geometrically nonlinear theory of elastic plates." J. Appl. Mech., ASME, 60, 109-116.
Hsiao, K. M.,(1987), "Nonlinear analysis of general shell structures by flat triangular shell element," Computer & Structures, Vol. 25, No. 5, pp. 665-675.
Horrigome, G., Bergan, P. G..,(1978), "Nonlinear analysis of free-form shell by flat finite elements," Computer Methods in Applied Mechanics and Engineering, Vol. 16, pp. 11-35.
Kuo, S. R., Yang, Y. B.,(1995), "Tracing Postbuckling Paths of Structures Containing Multi-Loops," International Journal for Numerical Methods in Engineering, Vol. 38, No. 23, pp. 4053-4075.
Kuo, S. R., Chi, C. C., Yeih, W., and Chang, J. R.,(2006), "A Reliable Three-Node Triangular Plate Element Satisfying Rigid Body Rule and Incremental Force Equilibrium Condition," Journal of the Chinese Institute of Engineers, Vol.29, No. 4, pp. 619-632
Krayterman, B. and Sabnis,G.,(1985), "Large Deflected Plates And Shells With Loading History," J. Engrg. Mech., ASCE, Vol. 111,No.5 ,pp. 393-401.
Levy, R., Gal, E.,(2001), "Geometrically nonlinear three-node flate triangular shell elements," Computers and Structures, Vol. 79, pp. 2349-2355.
Luo, Y. F. and Teng, J. G.,(1998), "Stability analysis of shells of revolution on nonlinear elastic foundations," Computers and structures. Vol. 69, pp. 449-511.
Mattiasson, K., (1981), "Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals", Int. J. Numer. Meth. Eng., Vol. 17, No. 1, pp. 145-153.
Meek, J. L., Tan, H. S.,(1986), "Instability analysis of thin plate and arbitrary shell using a faceted shell element with loof nodes," Computer Methods in Applied Mechanics and Engineering, Vol. 57, pp. 143-170.
Shen, H. S.,(1999), "Postbuckling of Reissner-Mindlin plate under biaxial compression and lateral pressure and resting on elastic foundations," Comput. Methods Appl. Mech. Engrg, Vol. 173, pp. 135-146.
Shen, H. S.,(1995), "Postbuckling of orthotropic plantes on two-parameter elastic foundation," J. Engrg. Mech., ASCE, Vol. 121, No. 1, pp. 50-56.
Shahwan, K. W. and Waas,A.M.,(1998), "Buckling of unilaterally constrained infinite plates."J. Engrg. Mech., ASCE, Vol. 124, No. 2, pp.127-136.
Timoshenko, S.P. and Woinowsky-Krieger, S.,(1959). Theory of Plates and Shells, 2nd ed. McGraw-Hill Book Co., New York.
Timoshenko, S.P. and Gere, J. M.,(1961). Theory of Elastic Stability, 2nd Ed., McGraw-Hill Book Co., New York.
Ugural, A. C.,(1981). Stresses in plates and shells, McGraw-Hill, New York.
Timoshenko, S.P. and Gere, J. M., (1972) “Mechanics of materials" Van Nostrand Reinhold Co., New York.
Wang, C. M., Kitipornchai, S. and Xiang, Y. and Liew, K. M.,(1993), "Stability of skew Mindlin Plates under Isotropic in-plane pressure," J. Engrg. Mech., ASCE, Vol. 119, No. 2, pp. 393-401.
Wempner, G.,(1981). Mechanics of solids with applications to thin bodies. Sijthoff & Noordhoff., Rockville, Mryland, U.S.A.
Wsshizu, K.,(1975). Variational method in elasticity and plasticity, 2nd 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, pp. 451-469.
Xiang, Y.,(2003), "Exact Solutions for Buckling of Multispan Rectangular Plates." J. Engrg. Mech., ASCE, Vol. 129, No. 2, pp. 181-187.
Yang, Y. B., Chiou, H. T.,(1987), "Rigid body motion test for nonlinear analysis with beam elements," Journal of Engineering Mechanics ASCE, Vol. 113, No.9, pp. 1404-1419.
Yang, Y. B., Shieh, M. S.,(1990), "Solution method for nonlinear problems with multiple critical points," AIAA Journal, Vol. 28, No. 12, pp. 2100-2116.
Yang, Y. B., and Kuo, S. R.,(1991), "Consistent Frame Buckling Analysis by Finite Element Method," Journal of Structural Engineering, ASCE, Vol. 117, No. 4, pp. 1053-1069.
Yang, Y. B., Kuo, S. R.,(1992), "Frame buckling analysis with full consideration of joint compatibilities," Journal of Engineering Mechanics. ASCE, Vol. 118, No. 5, pp. 871-889.
Yang, Y. B., Kuo, S. R.,(1994),Theory and Analysis of Nonlinear Framed Structures, Prentice-Hall, Singapore.
Yang, Y. B., Chang, J. T., Yau, J. D.,(1999), "A simple nonlinear triangular plate element and strategies of computation for nonlinear analysis," Computer Methods in Applied Mechanics and Engineering, Vol. 178, pp. 307-321.
Zheng, X. J. and Zhou, Y. H.,(1988), "exact solution of nonlinear circular plate on elastic foundation," J. Engrg. Mech., ASCE, Vol. 114 , No.8 ,pp. 1303-1316
Zhu, J. F.,(1995), "A new consideration on the derivation of geometrical stiffness matrix with the natural approach," Computer Methods in Applied Mechanics and Engineering, Vol. 123, pp. 141-160.
Ziegler, H.,(1977). Principles of structural stability. 2nd ed., Birkhäuser Verlag Basel, und Stuttgart.
Zienkiewicz, O. C., and R.L. Taylor., (1991), The finite element method McGraw-Hill, London ; New York
張健財, "幾何非線性三角形板元素的推導與應用之探討" , 國立臺灣大學土木工程研究所博士論文, 1997
林詩渤,"簡易非線性三角板元素" , 國立臺灣大學土木工程研究所碩士論文, 2005
郭世榮, "空間構架的靜力及動力及動力穩定理論", 國立臺灣大學土木工程研究所博士論文, 1991
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