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研究生:鍾昆潤
研究生(外文):Kun-Jun Chung
論文名稱:非耦合隱式動力有限元素分析 及其於結構崩塌分析之應用
論文名稱(外文):Decoupled-implicit-dynamic finite element analysis and its applications on structural collapse simulation
指導教授:李姿瑩李姿瑩引用關係
指導教授(外文):Tzu-Ying Lee
學位類別:博士
校院名稱:國立中央大學
系所名稱:土木工程學系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:146
中文關鍵詞:動態非線性分析地震力增量迭代程序等效節點割線勁度黏滯阻尼非耦合方程崩塌橋梁
外文關鍵詞:dynamic nonlinear analysisseismic loadingincremental-iterative procedureequivalent nodal secant stiffnessviscous dampingdecoupled equationscollapsebridge
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目前性能設計中如何驗證所設計之構造物遭遇不同強度地震時是否符合預期之性能目標,仍為極待解決之課題。尤其當結構物在極大地震力下有可能發生倒塌之情況,倒塌前結構物會經歷材料降伏、開裂和構件破斷,此狀態屬於高度非線性與不連續之問題。本研究提出一簡單且穩健的分析方法,可有效率地分析高度非線性與不連續結構系統於地震力作用下之反應。本研究提出等效節點割線勁度之概念,用以對角化勁度矩陣,並假設集中質量使平衡方程解耦。分析流程中採用隱式Newmark方法求解,並於每時間步幅中建立增量迭代程序,確保平衡方程中之不平衡力達收斂。此外,本文亦提出等效節點割線阻尼係數之概念對角化勁度阻尼矩陣,並說明如何快速計算非線性元素中與速度相依之阻尼力。並結合混合式時間積分方法(composite scheme)求解含剛體構件系統之運動問題,詳細探討此分析方法實際執行時之數值特性。研究成果顯示所提出之分析方法於穩定性、精確度、收斂性及計算效率方面皆有良好成效。

此外,2008年日本岩手縣內陸南部發生強震,導致祭畤大橋崩塌。本研究以祭畤大橋為例建立其數值模型進行結構崩塌分析,模擬此橋於強震中崩塌之破壞歷程,重現橋梁破壞過程,分析結果與當時橋梁真實破壞情況一致,驗證本研究所提出之分析方法確實能有效地分析實尺寸橋梁於極限狀態下之動態反應,並評估其於強震下之性能表現,藉以釐清瞭解橋梁破壞機制與緣由,提供未來橋梁規劃與耐震設計之參考。
This study presents a dynamic analysis procedure for predicting the responses of large, highly nonlinear, discontinuous structural systems subjected to seismic loading. The concept of equivalent nodal secant stiffness is proposed to diagonalize the conventional stiffness matrix of the structure. With the lumped-mass idealization, the decoupled equilibrium equations of the structure are then solved by the implicit Newmark integration method. Additionally, an incremental-iterative procedure is performed to ensure that the equilibrium conditions are satisfied at the end of each time step. Through extensive applications, the results demonstrate that the proposed procedure is simple and robust for analyzing practical structural systems in terms of computational efficiency and stability.

The concept of equivalent nodal secant damping coefficients is proposed to diagonalize the stiffness-proportional damping matrix. Additionally, a novel method is proposed to rapidly evaluate stiffness-proportional damping nodal forces for nonlinear elements on the element level. With the assumption of lumped-mass idealization an incremental-iterative procedure is performed to solve the decoupled equilibrium equations for damped systems using the implicit Newmark integration scheme and the composite integration scheme. The numerical results reveal that the characteristics of the proposed analysis procedure result in a robust method for solving structural dynamics systems to be achieved.

The dynamic analysis procedure is extended to simulate the seismic-induced collapse of bridges. Nonlinear and discontinuous behavior, such as material yielding, member damage, separation, falling and collision with other members, are considered in the analysis procedure. Additionally, multiple-support excitation is managed by using the equations of motion in the absolute coordinates. The Matsurube Bridge which collapsed in the 2008 Japan Iwate-Miyagi inland earthquake due to not only strong ground excitations but also sliding of underneath rock mass is analyzed for verifying the applicability of the proposed procedure. Through reproducing the in-situ collapse situation, the failure mechanisms of the bridge are identified. The results also demonstrate that the novel implicit dynamic procedure is superior in analyzing the collapse of bridges that exhibit highly nonlinear and discontinuous behaviors under extreme earthquakes.
TABLE OF CONTENTS

Abstract
Acknowledgements
Table of Contents I
List of Tables IV
List of Figures V
Nomenclature VIII
Chapter 1 Introduction 1
1.1 Problem Statement 1
1.2 Literature Review 3
1.2.1 Explicit Time Integration Scheme 3
1.2.2 Implicit Time Integration Scheme 4
1.2.3 Analysis of Structural Collapse 6
1.3 Objectives 7
1.4 Dissertation Outline 8

Chapter 2 Nonlinear Dynamic Analysis Procedure of Structures under Seismic Loading Based on Equivalent Nodal Secant Stiffness 10
2.1 Introduction 10
2.2 Incremental-Iterative Equations of Implicit Integration Method 11
2.3 Equivalent Nodal Secant Stiffness 12
2.4 Solution Procedure of Newmark Integration Method 14
2.5 Evaluation of Internal Element Nodal Force 15
2.5.1 Planar Beam Element 18
2.5.2 Four-Node Plane Element 18
2.6 Solution Based on Proposed Analysis Procedure 19
2.6.1 Stability and Accuracy 19
2.6.2 Convergence 20
2.6.3 Numerical Evaluation 20
2.6.4 Structures Modeled by Structural or Solid Elements 24
2.7 Discussion 26
2.8 Conclusions 27

Chapter 3 Nonlinear Dynamic Analysis Procedure with Damping Included 40
3.1 Introduction 40
3.2 Incremental-Iterative Equations with Damping Included 40
3.3 Equivalent Nodal Secant Damping Coefficient 44
3.4 Solution Procedure of Newmark Implicit Integration Method 45
3.5 Evaluation of Internal Element Nodal Force 47
3.5.1 Planar Bernoulli Beam Element 50
3.5.2 Four-Node Plane Element 51
3.6 Solution Based on Proposed Analysis Procedure 52
3.6.1 Stability, Accuracy and Convergence 52
3.6.2 Numerical Evaluation 53
3.6.3 Structures Modeled by Structural or Solid Elements 57
3.7 Discussion 60
3.8 Conclusions 61

Chapter 4 Nonlinear Dynamic Analysis Using Implicit Time Integration Schemes 75
4.1 Introduction 75
4.2 Nonlinear Dynamic Analysis Procedure 76
4.2.1 Decoupled Dynamic Incremental-Iterative Equation 76
4.2.2 The Composite Time Integration Scheme 79
4.3 Demonstrative Examples 81
4.3.1 The ‘Model Problem’ 81
4.3.2 The Flexural Pendulum due to Gravity 82
4.3.3 The Reinforced-Concrete Frame due to Seismic Loading 83
4.4 Conclusions 84

Chapter 5 Seismic-Induced Collapse Simulation of Bridges Using Implicit Dynamic Finite Element Procedure 93
5.1 Introduction 93
5.2 Implicit Dynamic Finite Element with Decoupled Equations 94
5.3 Link and Support Elements 95
5.3.1 Bilinear Plastic Model 96
5.3.2 Coulomb-Damped Model 96
5.3.3 Pounding at Expansion Joints 97
5.3.4 Impact at Arbitrary Locations 98
5.3.5 Unseating and Fracture of Structural Members 99
5.4 Multiple-Support Excitation 100
5.5 Numerical Model 102
5.5.1 Girders, Abutments and Columns 102
5.5.2 Bearings 103
5.5.3 Pounding and Impact 103
5.5.4 Passive Earth Pressure 104
5.5.5 Structural Damping 105
5.5.6 Multiple-Support Input Ground Motions 105
5.6 Progressive Collapse Mechanism during Earthquake 106
5.7 Conclusions 109

Chapter 6 Conclusions 120
6.1 Conclusions 120
6.2 Future Work 123

References 124
Anagnostopoulos SA. Pounding of buildings in series during earthquakes. Earthquake Engineering & Structural Dynamics 1988; 16(3): 443-456.
Bathe KJ, Wilson EL. Stability and accuracy analysis of direct integration methods. Earthquake Engineering & Structure Dynamic 1973; 1(3): 283-291.
Bathe KJ. Finite element procedures. Prentice-Hall: Englewood Cliffs, New Jersey; 1996.
Bathe KJ, Baig MMI. On a composite implicit time integration procedure for nonlinear dynamics. Computers & Structures 2005; 83(31-32): 2513-2524.
Bathe KJ. Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme. Computers & Structures 2007; 85(7-8): 437-445.
Bathe KJ, Noh G. Insight into an implicit time integration scheme for structural dynamics. Computers & Structures 2012; 98-99: 1-6.
Battini JM. A non-linear corotational 4-node plane element. Mechanics Research Communications 2008; 35(6): 408-413.
Belytschko T, Hsieh BJ. Non-linear transient finite element analysis with convected co-ordinates. International Journal for Numerical Method in Engineering 1973; 7(3): 255-271.
Bi K, Ren WX, Cheng PF, Hao H. Domino-type progressive collapse analysis of a multi-span simply-supported bridge: A case study. Engineering Structures 2015; 90: 172-182.
Borst R, Crisfield MA, Remmers JJC, Verhoosel CV. Non-linear finite element analysis of solids and structures (2nd edn). John Wiley & Sons: West Sussex; 2012.
Bui Q. V., Modified Newmark family for non-linear dynamic analysis. Int. J. Numer. Methods Eng. 2004; 61: 1390-1420.
Chang H. Geometrically nonlinear dynamic analysis with plane solid elements. Master thesis, National Central University, Taoyuan; 2016. (in Chinese)
Chang SY. A new family of explicit methods for linear structural dynamics. Comput. Struct. 2010; 88: 755-772.
Chang SY. Comparisons of structure-dependent explicit methods for time integration Int. J. Struct. Stability Dyn. 2015; 15(3): 1450055(1-20).
Chen CR. An analysis method for simulating the ultimate collapse of bridges. Master thesis, National Central University, Taoyuan; 2016. (in Chinese)
Chopra AK. Dynamics of structures: theory and applications to earthquake engineering (4th edn). Prentice-Hall: Englewood Cliffs, New Jersey; 2012.
Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- method. Journal of Applied Mechanics 1993; 60(2): 371-375.
Clough RW, Penzien J. Dynamics of structures (2nd edn). McGraw-Hill: Singapore; 1993.
Crisfield MA, Moita FG. A co-rotational formulation for 2-D continua including incompatible modes. Int. J. Numer. Methods Eng. 1996; 39(15): 2619-2633.
Cundall P, Strack ODL. A discrete numerical model for granular assemblies. Géotechnique 1979; 29(1): 47-65.
Dokainish MA, Subbaraj K. A survey of direct time-integration methods in computational structural dynamics – I. explicit methods, Computers & Structures 1989; 32(6): 1371-1386.
FEMA P-1050-2. NEHRP recommended seismic provisions for new buildings and other structures, Volume II: Part 3 resource papers. Washington (DC): Federal Emergency Management Agency; 2015.
Fujikake K, Li B, Soeun S. Impact response of reinforced concrete beam and its analytical evaluation. Journal of Structural Engineering 2009; 135(8):938-950.
Ghobarah A, Aziz TS, El-Attar M. Response of transmission lines to multiple support excitation. Engineering Structures 1996; 18(12): 936-946.
Ghobarah A. Performance-based design in earthquake engineering: state of development. Engineering Structures 2001; 23(8): 878-884.
Gravouil A, Combescure A. Multi-time-step explicit-implicit method for non-linear structural dynamics. Int. J. Numer. Methods Eng. 2001; 50: 199-225.
Hall JF. Problems encountered from the use (or misuse) of Rayleigh damping. Earthquake Engineering & Structure Dynamic 2006; 35(5): 525-545.
Hao H, Duan X. Multiple excitation effects on response of symmetric buildings. Engineering Structures 1996; 18(9): 732-740.
Hilber HM, Hughes TJR, Taylor RL. Improved numerical dissipation for the time integration algorithms in structural dynamics. Earthquake Engineering & Structure Dynamic 1977; 5(3): 283-292.
Ibarra LF, Medina RA, Krawinkler H. Hysteretic models that incorporate strength and stiffness deterioration, Earthquake Engineering & Structure Dynamic 2005; 34(12): 1489-1511.
Ishikawa M, Okuyama Y, Niizeki H. Simulation of collapsed bridge under an intense earthquake. Tohoku Society for the Promotion of Concrete Technology, Sendai, Japan; 2010. (in Japanese)
Isobe D, Tsuda M. Seismic collapse analysis of reinforced concrete framed structures using the finite element method. Earthquake Engineering & Structural Dynamics 2003; 32(13): 2027-2046.
Japan Road Association. Design specifications of highway bridges, Part V seismic design, Maruze, Tokyo; 2012.
Jia C, Leng Z, Li Y, Xia H, Liu L. Partitioned integration method based on Newmark’s scheme for structural dynamic problems. Int. J. Struct. Stab. Dyn. 2016; 16(1): 1640009(1-16).
Kawashima K, Penzien J. Theoretical and experimental dynamic behaviour of a curved model bridge structure. Earthquake Engineering & Structural Dynamics 1979; 7(2): 129-145.
Kim W, Reddy JN. An improved time integration algorithm: a collocation time finite element approach. Int. J. Struct. Stab. Dyn. 2017; 17(2): 1750024(1-38).
Kojic M, Bathe KJ. Inelastic analysis of Solids and Structures. Springer: Berlin;2005.
Kuhl D, Crisfield MA. Energy-conserving and decaying algorithms in nonlinear structural dynamics. International Journal for Numerical Methods in Engineering 1999; 45(5): 569-599.
Kuhl D, Ramm E. Constraint energy momentum algorithm and its application to nonlinear dynamics of shells. Computer methods in Applied Mechanics and Engineering 1996; 136(3-4): 293-315.
Kun F, Herrmann HJ. A study of fragmentation process using a discrete element method. Computer Methods in Applied Mechanics and Engineering 1996; 138(1-4): 3-18.
Kuo SR, Yau JD, Yang YB. A robust time-integration algorithm for solving nonlinear dynamic problems with large rotations and displacements. Int. J. Struct. Stab. Dyn. 2012; 12(6): 1250051(1-24).
Lee TY, Chung KJ, Chang H. A new implicit dynamic finite element analysis procedure with damping included. Engineering Structures 2017; 147: 530-544.
Lee TY, Chung KJ, Chang H. A new procedure for nonlinear dynamic analysis of structures under seismic loading based on equivalent nodal secant stiffness, Int. J. Struct. Stab. Dyn. 2018; 18(3): 1850043.
Li J, Spencer BF, Elnashai AS, Phillips BM. Substructure hybrid simulation with multiple-support excitation. Journal of Structural Engineering 2012; 138(7): 867-876.
Lu X, Lu XZ, Guan H, Ye L. Collapse simulation of reinforced concrete high-rise building induced by extreme earthquakes. Earthquake Engineering & Structural Dynamics 2013; 42(5): 705-723.
Lynn KM, Isobe D. Finite element code for impact collapse problems of framed structures. International Journal for Numerical Methods in Engineering 2007; 69(12): 2538-2563.
Nazmy AS, Abdel-Ghaffar A. Non-linear earthquake-response analysis of long-span cable-stayed bridges: theory. Earthquake Engineering & Structural Dynamics 1990; 19: 45-62.
Pekau OA, Cui Y. Progressive collapse simulation of precast panel shear walls during earthquakes. Computers & Structutes 2006; 84(5-6): 400-412.
Portioli F, Cascini L. Large displacement analysis of dry-jointed masonry structures subjected to settlements using rigid block modelling. Engineering Structures 2017; 148: 485-496.
Priestley MJN. Performance based seismic design. Proceedings of 12th World Conference on Earthquake Engineering: Auckland, New Zealand; 2000.
Rezaiee-Pajand M, Hashemian M. Time integration method based on discrete transfer function. Int. J. Struct. Stability Dyn. 2016; 16(5): 1550009(1-22).
Rezaiee-Pajand M, Karimi-Rad M. A new explicit time integration scheme for nonlinear dynamic analysis. Int. J. Struct. Stability Dyn. 2016; 16(9): 1550054(1-26).
Rice DL, Ting EC. Large displacement transient analysis of flexible structures. International Journal for Numerical Method in Engineering 1993; 36(9): 1541-1562.
Sakai J, Unjoh S, Hoshikuma J, Zhang G. Damage of Mazurube bridge collaped in the 2008 Iwate-Miyagi inland earthquake and its response characteristics. Proceedings of 3rd Symposium on Records and Topics for Great Earthquakes Occurred in Japan and Overseas, Japan Society of Civil Engineers, Tokyo, Japan; 2010. (in Japanese)
Salem HM, Helmy HM. Numerical investigation of collapse of the Minnesota I-35W bridge. Engineering Structures 2014; 59: 635-645.
Seismic Design Group. Unseating Mechanism of Mazurube bridge. Kyushu Institute of Technology, Fukuoka, Japan; 2008. (in Japanese)
Shames IH. Engineering Mechanics, Vol II Dynamics (3rd edn). Prentice-Hall, New Jersey; 1980.
Shih C, Wang YK, Ting EC. Fundamentals of a vector form intrinsic finite element: Part III. Convected material frame and examples. Journal of Mechanics 2004; 20(2): 133-143.
Simo JC, Tarnow N. The discrete energy-momentum method. Conserving algorithm for nonlinear elastodynamics. Journal of Applied Mathematics and Physics 1992; 43(5): 757-792.
Sivaselvan MV, Lavan O, Dargush GF, Kurino YH, Fukuda R, Sato K, Apostolakis G, Reinhorn AM. Numerical collapse simulation of large-scale structural systems using an optimization-based algorithm. Earthquake Engineering & Structural Dynamics 2009; 38(5): 655-677.
Subbaraj K, Dokainish MA. A survey of direct time-integration methods in computational structural dynamics – II. implicit methods, Computers & Structures 1989; 32(6): 1387-1401.
Ting EC, Shih C, Wang YK. Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a plane frame element. Journal of Mechanics 2004; 20(2): 113-122.
Ting EC, Shih C, Wang YK. Fundamentals of a vector form intrinsic finite element: Part II. Plane solid elements. Journal of Mechanics 2004; 20(2): 123-132.
Tirasit P, Kawashima K. Effect of nonlinear seismic torsion on the performance of skewed bridge piers. Journal of Earthquake Engineering 2008; 12(6):980-998.
University of California at Berkeley. SAP2000, Integrated finite analysis and design of structures, analysis reference manual (Version 11.0.8). Computers and structures, Inc., California, USA; 2007.
Wang G, Wang Y, Lu W, Yu M, Wang C. Deterministic 3D seismic damage analysis of Guandi concrete gravity dam: A case study. Engineering Structures 2017; 148: 263-276.
Warburton GB, Soni SR. Errors in response calculations for non-classically damped structures. Earthquake Engineering & Structure Dynamic 1977; 5(4): 365-376.
Wen YK. Method for random vibration of hysteretic system, ASCE Journal of the Engineering Mechanics Division 1976; 102(2): 249-263.
Wu JH. New edge-to-edge contact calculating algorithm in three-dimensional discrete numerical analysis. Advances in Engineering Software 2008; 39(1): 15-24.
Yang YB, Chiou HT. Rigid body motion test for nonlinear analysis with beam elements. Journal of Structural Engineering 1991; 117(4):1053-1069.
Yang YB, Kuo SR, Wu YS. Incrementally small-deformation theory for nonlinear analysis of structural frames. Engineering Structures 2002; 24(6):783-798.
Yang YB, Lin SP, Chen CS. Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation. Computer Methods in Applied Mechanics and Engineering 2007; 196(7): 1178- 1192.
Yin SH. A new explicit time integration method for structural dynamics. International Journal of Structural Stability and Dynamics 2013; 13(3): 1250068(1-23).
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