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研究生:蕭邦安
研究生(外文):Pang-An Hsiao
論文名稱:非彈性結構大變形之數值模擬
論文名稱(外文):NUMERICAL MODELING FOR INELASTIC STRUCTURES WITH LARGE DISPLACEMENT
指導教授:邱耀正邱耀正引用關係
指導教授(外文):Yaw-Jeng Chiou
學位類別:博士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
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:2003
畢業學年度:91
語文別:英文
論文頁數:183
中文關鍵詞:移動參考構架法顯性有限元素法非彈性結構個人電腦叢集
外文關鍵詞:Explicit finite elementConvected material frame approach
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本文應用移動參考構架法(Convected Material Frame Approach, CMF)並改變分析流程中的組成律,文中材料之應力應變關係以非線彈性函數表示,使之可以針對不同的材料特性進行非線彈性結構的暫態、擬靜態分析及受反覆載重下的力學行為進行探討,本研究亦模擬結構於高溫火場環境的力學行為,本文並應用MPI (message passing interface)進行平行計算之研究。其目的在以叢集技術為架構的平行電腦上,探討平行計算的可行性與評估其效能,進而推廣平行處理的高效能計算環境。
移動參考構架法在分析的方法上是源於傳統的顯性有限元素法並將之改良而成。本方法將求解的過程離散化,先針對結構物將其化成有限個元素的集合,接著取前後分析時間點的變形差,求解桿件元素上的應力應變關係,再由此關係利用虛功原理求解結構動力平衡方程式,並輔以顯性時間積分法,以求解結構物在各歷時下的變位、速度與加速度;在分析時,利用微小時距間小變形的假設來模擬大變形問題,以避免數值運算上的問題。文中材料之應力應變關係以非線彈性函數表示,結果顯示移動參考構架法可合理地模擬結構大變形行為。
現行耐震設計大多利用非彈性行為以消散能量的概念去做設計。在高樓部份也廣泛應用鋼構斜撐來做為消散能量的方式。因此,對於鋼結構從受力到破壞的行為模式及鋼結構受反覆載重下的非彈性大變形分析為必要課題。本文利用移動參考構架法模擬結構的非幾何大變形行為並採用Dafalis-Popov Two-Surface Model (TSM)描述鋼構造受反覆荷重下的材料行為,結果顯示移動參考構架法可合理模擬鋼結構受反覆載重下的大變形行為,此外,本文亦採用澳洲規範描述高溫環境下之鋼結構的材料性質,結果顯示移動參考構架法可合理地模擬高溫環境下結構大變形行為。本研究並應用MPI進行不同平行電腦平台下平行計算效能分析,目的在以叢集技術為架構的平行電腦上,探討平行計算的可行性與評估其效能,平行計算的執行主要在國家高速電腦中心(NCHC)所提供的IBM SP2及電腦叢集(PC Clusters)執行並應用MPI進行不同平行電腦平台下平行計算效能分析結果顯示計算效能隨處理器數量增加而提升,並顯示移動參考構架法適用於進行平行處理且加速比隨處理器數量增加而提升。
This study presents the convected material frame approach to study the nonlinear behavior of inelastic frame structures. The convected material frame approach is a modification of the co-rotational approximation by incorporating an adaptive convected material frame in the basic definition of the displacement vector and strain tensor. In the formulation, each discrete element is associated with a local coordinate system that rotates and translates with the element. For each load increment, the corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and based on the updated element geometry. The rigid body motion and deformation displacements are decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through the continuous updating of the material frame geometry. A generalized nonlinear function is used to derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in the analysis by assuming a lumped mass matrix of diagonal form.
Many features of the adopted approach are presented in this research. For the purpose of considering the gradual plastification through the cross section and along the member length, the Bauschinger effect, strain hardening and residual stresses produced during hysteretic plastic deformation, the convected material frame approach adopted the Dafalis-Popov two-surface model analyze the nonlinear cyclic plasticity behavior of the steel frames in this research. The structures subjected to horizontal triangular wave load, sine wave load, earthquake load, and horizontal harmonic wave load are studied. The numerical results show that the present approach is capable of simulating the nonlinear transient responses of frame structures.
The convected material frame approach is presented for analysis of nonlinear behavior of steel frames subjected to fire in the present study. The material and geometrical non-linearity as well as the uniform profile of temperature across section of frame members are taken into account. In recent years the rapid development of computer hardware environments with parallel processing capabilities has created new opportunities for revolutionizing engineering computing. The constant improvement of price/performance ratio of commodity computing hardware, coupled with the innovation of networking technology, has made cluster computing one of the most attractive computing architectures for both academic institutes and industrial organizations in the last several years. Therefore, this study investigates a parallel processing strategy for simulations of nonlinear behavior of inelastic structures. A parallel explicit finite element approach is employed to facilitate inelastic structural analysis more efficient. All the computation is carried out on the PC clusters in Linux and conventional parallel machine IBM SP2 at the National Center for High-Performance Computing (NCHC), Hsinchu, Taiwan. The message passing software package, MPI, is utilized as a parallel construct for data communication and message passing among processors.
Several numerical examples are demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show that the proposed approach is capable of investigating large deflection of inelastic planar structures and providing an excellent numerical performance. The performance parallel computation studies indicate that this explicit algorithm is highly adaptive for parallel processing.
摘要I
Abstract II
致謝IV
Table of Contents V
List of Tables VIII
List of Figures IX
Chapter 1 Introduction
1.1 Overview 1
1.2 Objectives 3
Chapter 2 Large displacement analysis of inelastic frame structures by convected material frame approach
2.1. Introduction 5
2.2. Formulation of the convected material frame approach 6
2.2.1 Coordinates 7
 2.2.2 Kinematics 7
 2.2.3 Principle of virtual work 10
 2.2.4 Explicit time integration 14
2.3. Numerical examples and discussion 17
 Example 1. Cantilever beam with a tip load 17
 Example 2. Rigid frame subjected to a quasi-static horizontal load 17
 Example 3. Rigid frame subjected to a dynamic horizontal load 18
 Example 4. Rigid frame subjected to quasi-static horizontal and vertical loads 18
 Example 5 Clamped-roller beam subjected to a vertical load at middle point 18
 Example 6. Three-story four-bay frame subjected to one cycle triangle-wave horizontal load 19
2.4. Conclusions 19
Chapter 3 Large displacement analysis of cyclically loaded inelastic structures
3.1 Introduction 44
3.2 General Description of Uniaxial Loading in Two-surface model 46
3.3 Numerical Simulation
 Example 1 Clamped-roller beam subjected to a vertical triangle wave load at middle point 50
 Example 2 Simply- supported beam subjected to a vertical triangle wave cyclic load at middle point 50
 Example 3. Clamped-roller beam subjected to a vertical sine-wave cyclic load at middle point 51
 Example 4. Rigid frame subjected to a horizontal triangle wave cyclic load 51
 Example 5. One-story rigid frame subjected to sine wave cyclic loading 51
 Example 6.One-story rigid frame subjected to a quasi-half-sine impulse cyclic load 52
 Example 7. Rigid Frame subjected to an earthquake ground motion 52
 Example 8. Three-story four-bay frame subjected to various triangle-wave cyclic load histories 52
 Example 9. Three-story four-bay frame subjected to various horizontal harmonic wave load histories 53
 Example 10. Eight-story four-bay frame subjected to a horizontal load 53
 Example 11 Ten-story four-bay frame subjected to a horizontal ramp load 53
 Example 12. Ten-story eight-bay frame subjected to a horizontal ramp load 54
3.6 Conclusions 54
Chapter 4 Nonlinear analysis for two-dimensional steel frames in elevated temperature conditions
4.1Introduction 109
4.2Mechanical Properties of steel at elevated temperature 110
4.3Bilinear model hypothesis 111
4.4 Coefficient of thermal expansion 112
4.5Acceptance Criteria 112
4.6Verification of fire analysis capability 113
 Example1. One-story steel frame at elevated temperature 113
 Example2. Two-story steel frame exposed to localized fire at the first floor 114
 Example3. Two-story steel frame exposed to localized fire at the second floor 115
 Example4. Simply supported beam subject to uniform elevated temperatures 115
4.7 Conclusions 116
Chapter 5 Parallel computation of large displacement analysis of inelastic structures by pc clusters
5.1. Introduction 138
5.2 Implementation of parallel computation for convected material approach 140
5.2.1 Parallel computing environment 140
5.2.2 Parallel implementation of CMF approach 141
5.3 Numerical examples and discussion 143
 Example1: Simply supported I-section beam subjected to a concentrated load at mid-span 143
 Example 2: Rigid frame subjected to a quasi-static horizontal load 144
 Example3 Rigid frame subjected to a dynamic horizontal load 145
 Example 4. Eight-story four-bay frame subjected to a horizontal ramp load 145
 Example 5. Ten-story eight-bay frame subjected to a horizontal ramp load 146
5.4 Conclusions 147
Chapter 6 Conclusions 169
List of References 172
Appendix A. Derivation of Deformation Displacements Related to Nodal Displacements by Shape Functions 178
Appendix B. Inelastic materials performed by Gaussian quadrature method 180
Appendix C. Derivation of Eq.(2.28) by Central Difference 183
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