Nonlinear Analysis of Reinforced Concrete Structures using The Novel Implicit Nonlinear Dynamic Finite Element method

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姓名	阮青俊(Nguyen Thanh Tuan) 查詢紙本館藏	畢業系所	土木工程學系
論文名稱	Nonlinear Analysis of Reinforced Concrete Structures using The Novel Implicit Nonlinear Dynamic Finite Element method (Nonlinear Analysis of Reinforced Concrete Structures using The Novel Implicit Nonlinear Dynamic Finite Element method)
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摘要(中)	使用傳統方法對結構進行非線性動力分析非常耗時，尤其是對於塑鉸、構件破壞和結構倒塌等複雜問題。傳統的塑鉸模擬通常使用集中彈簧模型，不僅不能描述塑鉸區截面上纖維的應力應變關係，也不能考慮雙軸力矩和軸向載荷之間的相互作用。另一方面，纖維元素法可以合理地模擬圍束混凝土、無圍束混凝土和鋼筋的遲滯行為。然而，使用纖維元素在計算上是相當耗時的，因此在實踐中並不常實施。為了解決這個問題，本研究將纖維元素法引入到最近開發的新隱式非線性動力有限元法 (NINDFEM) 中，用於模擬三維鋼筋混凝土建築物受地震後的結果。為了驗證所提出的算法，通過非線性靜態和動態分析模擬了具有不同材料本構關係的多個模型。結果表顯示，所提出的方法可以準確地模擬塑鉸的非線性行為並主導計算效率。此外，所提出的模型可以在一個斷面中逐步描述不同纖維的破壞機制，這是Sap2000、Opensees等常規軟件無法實現的。
摘要(英)	The nonlinear dynamic analysis of structures using the traditional methods is very time-consuming especially for complex problems including plastic hinges, failure of components, and collapse of structures. The conventional simulation of plastic hinges usually uses concentrated spring models which cannot depict the stress-strain relationship of fibers on a cross-section in a plastic-hinge zone and cannot consider the interaction between biaxial moment and axial load. The fiber element method, on the other hand, can reasonably simulate the hysteretic behavior of confined concrete, unconfined concrete, and steel. However, using fiber elements is computationally expensive and hence is not often implemented in practice. To address it, this study introduces the fiber element method into the recently developed novel implicit nonlinear dynamic finite element method (NINDFEM) for simulating 3-D reinforced concrete buildings subjected to earthquakes. To verify the proposed algorithm, multiple models with different material constitutive relationships are simulated through nonlinear static and dynamic analyses. The result shows that the proposed method can accurately simulate the nonlinear behavior of plastic hinges and dominate the computational efficiency. Furthermore, the proposed model can progressively describe the failure mechanism of different fibers in a section, which cannot be achieved by conventional software, such as Sap2000, Opensees, etc.
關鍵字(中)	★ 新隱式非線性動力有限元方法 ★ 纖維 ★ 鋼筋混凝土模型 ★ 破壞 ★ 倒塌 ★ 非線性 ★ 動力分析 ★ 塑鉸	關鍵字(英)	★ Novel implicit nonlinear dynamic finite element method ★ fiber element ★ spring element ★ reinforced concrete models ★ failure ★ destruction ★ nonlinear ★ dynamic analysis ★ plastic hinge.
論文目次	摘要 i Abstract ii Acknowledgments iii Contents iv List of Figures vii List of Tables xi Chapter I Introduction 1 1.1 Research motivation and purpose 1 1.2 Literature review 2 1.2.1 The Novel implicit nonlinear dynamic finite element method. 2 1.2.2. Newmark integral method 3 1.2.3 HHT -alpha integral method 3 1.2.4 Fiber element method 4 1.3 Thesis structure 5 Chapter II Theory and Analysis Methods 6 2.1 The Novel implicit nonlinear dynamic finite element method. 6 2.1.1 Derivation of the Novel implicit nonlinear dynamic finite element method. 6 2.1.2. Implicit direct integration method 9 2.2. Spatial framework elements. 14 2.2.1. Local coordinate of elements 14 2.2.2. Element deformation and internal forces 19 2.2.3. Element stiffness damping force 23 2.2.4 Inertial and damping forces of the lumped mass of elements. 27 Chapter III The Fiber Element Method 34 3.1 Preface 34 3.2 Generalized definition of force and deformation. 34 3.3. The formulation for column-beam element. 35 3.4 Determine the state of the computation. 39 3.5 Fiber element parameters and models. 44 3.6 Basic formula of fiber elements. 46 3.7 Non-linear calculation process of fiber beam elements. 48 Chapter IV The reinforced concrete models 64 4.1. The bilinear model of reinforcement. 64 4.1.1 The required parameters for the model. 64 4.1.2 The rules for determining the state of stress and strain 64 4.2. The Kawashima model 67 4.2.1 The required parameters for the model. 67 4.2.2 The envelope curve of the model 67 4.2.3 The unloading path 68 4.2.4 The reloading path 69 4.3. The Mander model 71 4.3.1 The required parameters for the model. 71 4.3.2 The envelope curve of the model 71 4.3.3 The unloading path 72 4.3.4 The reloading path 73 Chapter V Verification of Numerical Examples 87 5.1 Pushover analysis. 87 5.1.1 Nonlinear behavior. 87 5.1.2 Failure behavior. 88 5.2. Dynamic analysis with Rayleigh damping 89 5.3. Dynamic analyses for frame systems 90 5.3.1. The plane frame building with two fiber elements. 90 5.3.2. The plane frame building with six fiber elements in beams and columns. 91 5.3.3. A 3-D one-story building with four fiber elements. 92 5.3.4. A 3-D one-story building with sixteen fiber elements in beams and columns. 92 5.3.5. A 3-D five-story building with four fiber elements. 93 5.3.6. Summary of the chapter. 94 Chapter VI Fiber and Link element 141 6.1 X-ground motion. 141 6.2. Y-ground motion. 142 6.3. XYZ-ground motion. 142 Chapter VII Conclusion and potential future work 147 7.1. Conclusion. 147 7.2. Potential future work. 148 References 150
參考文獻	[1] Lee, T.Y., Chung, K.J. and Chang, H., "A new implicit dynamic finite element analysis procedure with damping included.," Engineering Structures, 147, pp. 530-544, 2017. [2] Lee, T.Y., Chung, K.J. and Chang, H., "A new procedure for nonlinear dynamic analysis of structures under seismic loading based on equivalent nodal secant stiffness," International Journal of Structural Stability and Dynamics, 18(3), 1850043, 2018. [3] N. M. Newmark, "A Method of Computation for Structural Dynamics," ASCE Journal of the Engineering Mechanics Division, vol. 85, pp. 67-94, 1959. [4] H. M. Hilber, T. J. R. Hughes, and R. L. Taylor, "Improved numerical dissipation for time integration algorithms in structural dynamics," Earthquake Engineering and Structural Dynamics, 5, p. 283–292, 1977. [5] 陳鵬宇, "橋梁三維極限破壞分析," 國立中央大學土木系碩士論文, 2013. [6] 王聖文, "含結構阻尼之三維非線性動力歷時分析," 國立中央大學土木系碩士論文, 2020. [7] Taucer, F. F., Spacone, E., and Filippou, F. C., "A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures," No. UCB/EERC-91/17, Earthquake Engineering Research Center, University of California, Berkeley, 1991. [8] Watanabe, G., Kawashima, K., "Numerical Simulation of Pounding of Bridge Decks," 13th World Conference on Earthquake Engineering, 2004. [9] Hoshikuma, J., Kawashima, K., Nagaya, K., and Taylor, A. W., "Stress-strain Model for Confined Concrete in Bridge Piers," ASCE, Journal of Structural Engineering, vol. 123, no. 5, 1997. [10] Sakai, J., Kawashima, K., "Unloading and Reloading Stress-Strain Model for Confined Concrete," ASCE, Journal of Structural Engineering, vol. 132, no. 1, 2006. [11] Mander, J. B., Priestley, M. J. N., and Park, R., "Theoretical Stress-Strain Model for Confined Concrete," ASCE, Journal of Structural Engineering, vol. 114, no. 8, 1988.
指導教授	李姿瑩陳鵬宇(Tzu-Ying, Lee Peng-Yu, Chen)	審核日期	2022-2-23
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