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研究生:徐偉朝
研究生(外文):Wei-chao Hsu
論文名稱:土壤與無限延伸結構互制系統之能量傳導邊界
論文名稱(外文):An Energy Transmitting Boundary for Soil and Semi-Infinite Structure Systems
指導教授:陳希舜陳希舜引用關係
學位類別:博士
校院名稱:國立臺灣科技大學
系所名稱:營建工程系
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:2006
畢業學年度:94
語文別:英文
論文頁數:169
中文關鍵詞:土壤結構互制無限延伸結構能量傳導邊界
外文關鍵詞:soil-structure interactioninfinite structureenergy transmitting boundary
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利用有限元素分析無限延伸結構系統時,常需建立龐大之分析模式,相當費時。根據部份結構法,無限延伸結構系統可分成有限區域與無限區域等兩部份。本文之主要目的係發展一能量傳導邊界,模擬結構系統之無限延伸區域。

為模擬結構無限延伸區域,本文發展出半無限延伸固體元素,根據虛功原理,建立土壤與半無限延伸結構系統之控制方程式,並建立傳導邊界之動態勁度,加於有限區域之邊界。僅須以有限區域之結構元素進行分析,可大幅減小分析模式。同時,本論文亦發展並驗證一套電腦程式,以模擬本文所提出之結構能量傳導邊界。

本文利用簡諧力作用於表面與埋置結構系統,獲得結構系統之垂直與水平動態反應,藉以驗證並展示本文所發展之電腦程式與結構能量傳導邊界之能力。經比較結構之動態反應顯示,利用本文所提出之結構能量傳導邊界能精確的模擬土壤結構互制系統之動態反應。因此,能大幅減小分析模式,並有效提昇運算效能。

本文所提出之結構能量傳導邊界可應用於公路、軌道、地下隧道及地下管線系統,以大幅減少動態分析所需之工作。
For the dynamic finite element analysis of an infinite structure system, it usually needs to establish a very large analytical model, which is very time-consuming. According to the substructure concept, the infinite structure can be divided into two substructures, a finite and a semi-infinite region. The main purpose of this dissertation is to develop an energy transmitting boundary to simulate the structural semi-infinite region.

To simulate the structural semi-infinite region, a semi-infinite solid element is developed. By the principle of virtual work, the governing equation of the soil and semi-infinite structure system is established. The dynamic stiffness at the transmitting boundary can then be established and added to the boundary of the finite region. Only the structural elements in the finite region are needed in the analysis, which can significantly reduce the analytical model. A computer program is also developed and verified for the proposed structural transmitting boundary.

The horizontal and vertical displacements of surface and embedded structure systems induced by harmonic excitations are investigated to demonstrate the capability of the developed computer program and the associated structural transmitting boundary. The results show that the proposed energy transmitting boundary can accurately obtain the dynamic responses of soil-structure systems. The analytical model size can also be largely reduced and the calculation performance be effectively enhanced.

The proposed energy transmitting boundary may be applied to highway, railway, subway, and buried piping systems to reduce the effort for dynamic analysis significantly.
Table of Contents. i
List of Tables v
List of Figures vi
List of Notations ix
1 Introduction 1
2. Dynamic Stiffness of a Soil-Structure Interaction System 3
2.1 Complex response representation 3
2.2 Equation of motion in the cylindrical coordinate system 4
2.3 Wave number 10
2.4 Governing equations of Rayleigh and Love waves 11
2.5 Axisymmetric transmitting boundary of a soil system 14
2.6 Axisymmetric element 16
2.6.1 Vertical load case 17
2.6.2 Horizontal load case 20
2.7 Impedance matrix of a soil system 22
2.8 Total stiffness matrix of the soil-structure system 23
3. Energy Transmitting Boundary for Semi-infinite Structures 25
3.1 Substructures 25
3.2 Semi-infinite solid element 26
3.3 Structural transmitting boundary .29
3.3.1 Internal virtual work of the semi-infinite solid elements 30
3.3.2 External virtual work of the structural transmitting boundary 31
3.3.3 External virtual work of soil-structure interaction 32
3.3.4 Dynamic stiffness matrix of the structural transmitting boundary 33
3.4 Total stiffness matrix of the soil-structure system 35
4. Computer Program and Verification 37
4.1 Calculation procedure 37
4.2 Program modules 39
4.3 Verification 42
5. Cases Study 44
5.1 Displacement amplitude 44
5.2 A vertical load applied at the edge of a semi-infinite plate 44
5.3 A vertical load applied at an infinite tunnel 46
5.4 Load applied at infinite pavement systems 48
5.5 Dynamic responses near an infinite pavement system 50
6. Conclusions 51
References 53
Appendix A Impedance Analysis for Multi-layered Soil Systems 131
A.1 Solutions of wave equations in the cylindrical coordinate 131
A.2 Governing equations of Rayleigh and Love wave motions 136
A.3 Boundary conditions 140
A.4 Modal shapes of Rayleigh wave motion 143
A.5 Modal shapes of Love wave motion 149
A.6 Axisymmetric transmitting boundary of a soil system 151
A.7 Displacements outside the transmitting boundary 157
Appendix B Derivation of Structural Transmitting Boundary 159
B.1 Semi-infinite solid element 159
B.2 Internal virtual work of the semi-infinite region 162
B.3 External virtual work of the structural transmitting boundary 165
B.4 External virtual work of the soil-structure interaction 166
B.5 Governing equation of the semi-infinite structure 167
B.6 Nodal force vector at the structural transmitting boundary 167
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