本研究的範圍是探討無網格相關數值方法，包括真無網格法(pure meshfree method)、耦合無網格法(meshfree methods)及網格法(mesh-based methods )應用於各種土壤與結構互制作用問題的有效方法評估。首先，吾人藉由探討無網格法的定義、分類及基本屬性，同時說明無網格法如何使用於科學計算領域，用以瞭解無網格法的發展趨勢。進而說明土壤與結構動力學的基本控制方程式，特別是波動方程式及結構動力非線性行為的數值和物理背景以及土壤與結構互制作用問題。其後，分別介紹兩個不同的無網格法的細節，即點插法(PIM)和無網格伽遼金法(EFGM)及其進一步發展，以解決土壤與結構互制作用的數值案例。再者為了採納無網格法和網格法的各自優點，並避免其各自缺點，推導兩種耦合的數值程序，並且介紹數個土壤與結構互制作用的代表計算例，並討論及證明新的無網格法的適用性和耦合方法，並與傳統網格法，獲得之結果相比較。在最後章節將提出本研究之結論與建議。

The scope of this dissertation is to develop, implement and investigate some meshfree-related approaches including the pure meshfree methods and the coupling of meshfree and meshbased methods with respect to an efficient solution of var ious soil-structure interaction problems. Therefore reviews the definition, classification, and basic properties of meshfree methods. It illustrates how meshfree methods can be used in the field of scientific computation, and discusses the trends of meshfree methods are evolving. Then, basic formulations in structural dynamics are given. In particular, the wave equations and the nonlinear formulation of a dynamically excited structure reveal the mathematical as well as physical backgrounds for most soil-structure interaction problems. Then, respectively, we introduce two different meshfree methods in detail, namely the PIM and the EFGM. These two meshfree methodologies are appropriately further developed by the writer in order to solve the numerical examples on soil-structure interaction. To better deploy the advantages from the meshfree and the mesh-based methods and avoid their respective drawbacks at the same time, two coupling procedures are worked out. Some representative examples of soil-structure interaction are discussed in detail to demonstrate the applicability of the new meshfree methods and the coupling approaches. The results are all well compared with those obtained by conventional mesh-based methods. Conclusions and future perspectives will be given in final Chapter.

論文審定書---------------------------------------iii
誌謝------------------------------------------------iv
中文摘要------------------------------------------v
英文摘要------------------------------------------vi
符號對照表---------------------------------------xiv
第一章 緒論--------------------------------------1
1.1 動機-------------------------------------------1
1.2 概述-------------------------------------------3
1.2.1 無網格法概念-----------------------------3
1.2.2 土壤與結構互制行為--------------------5
1.3 論文內容-------------------------------------6
第二章 無網格法基本原理--------------------8
2.1 無網格法的分類----------------------------9
2.1.1 公式化程序的分類----------------------9
2.1.2 擬合技法的分類------------------------11
2.1.3 離散技法的分類------------------------13
2.2 無網格法運算程序-----------------------14
2.2.1 基本步驟---------------------------------14
2.2.2 選定支持域------------------------------18
2.2.3 建立形狀函數---------------------------19
第三章 動力控制方程式----------------------21
3.1 線彈性動力方程式------------------------21
3.2 非線性結構動力分析---------------------24
3.2.1 線性簡化原理---------------------------24
3.2.2 系統離散化原理------------------------28
3.2.3 運算程序---------------------------------30
第四章 無網格點插法-------------------------33
4.1 多項式點插法------------------------------34
4.1.1 建立形狀函數----------------------------34
4.1.2 形狀函數特性----------------------------37
4.2 徑向式點插法------------------------------39
4.2.1 建立形狀函數----------------------------39
4.2.2 形狀函數特性----------------------------43
4.3 複合方程------------------------------------43
4.4 邊界型複合式點插法---------------------47
4.4.1 邊界型多項式點插法------------------48
4.4.2 邊界型徑向式點插法-------------------50
4.4.3 離散方程----------------------------------52
4.4.4 執行評估----------------------------------54
第五章 無網格伽遼金法-----------------------56
5.1 基本方程式---------------------------------56
5.1.1 建立形狀函數----------------------------57
5.1.2 形狀函數特性----------------------------60
5.2 移動式克里金插值法----------------------62
5.2.1 克里金插值原理-------------------------62
5.2.2 移動式克里金插值原理----------------66
5.2.3 關聯性的建置----------------------------68
5.2.4 移動式克里金插值法擬合特性-------69
第六章 耦合無網格法及網格法--------------71
6.1 無網格伽遼金法與有限元素法的耦合-71
6.1.1 交界面處理-------------------------------71
6.1.2 耦合之計算機演算法-------------------74
6.2 無網格伽遼金法與邊界元素法的耦合-76
6.2.1 交界面處理-------------------------------76
6.2.2 耦合的運算程序-------------------------77
第七章 數值算例--------------------------------80
7.1 懸臂樑----------------------------------------80
7.1.1 分析流程說明----------------------------81
7.1.2 靜力分析----------------------------------104
7.1.3 動力分析----------------------------------110
7.2 土壤與單樁互制---------------------------113
7.3 土壤與群樁互制---------------------------117
7.4 土壤與簡化海域平台互制---------------120
7.4.1 地震力------------------------------------122
7.4.2 波浪力------------------------------------123
7.4.3 分析結果---------------------------------124
第八章 結論與建議----------------------------129
8.1 結論------------------------------------------129
8.2 建議------------------------------------------131
參考文獻-----------------------------------------132
附錄-----------------------------------------------144
簡歷-----------------------------------------------153

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