臺灣博碩士論文加值系統

土木結構分析設計工作，發展能夠與極限設計匹配的方法——極限分析——是相當重要的課題。塑性的重要特徵就是「路徑對路徑」，位移與載重的關係是「路徑相關的」。一般來説，材料未降伏前存在著一個「初始降伏面」，隨著力量加載，材料切換至塑性的階段，隨著載重的路徑不同，會演化其對應的「接續降伏面」，接續降伏面是無窮多的，即不唯一，且與路徑相關。在安全載重與靜態崩塌之間，可以在載重空間建立唯一的「塑性極限面」，也就是說不必進行較冗長的塑性歷時歷程分析。

如果載重具有循環、重覆性，則在塑性變形下，可能有惡性的增量崩塌或交替降伏（塑性疲勞）的現象，也可能在適當的殘留應力分佈下，產生良性的安定現象。在安全循環載重與增量崩塌或交替降伏之間，可以在載重空間建立唯一的「安定極限面」，不必進行較冗長的塑性循環歷時分析。

本文主要在探討載重空間塑性極限面與安定極限面的計算方法，具有線彈性完全塑性組成模式，建構向量線性不等式，接著延伸線性代數的計算方法，使其適用於不等式計算，跳過接續降伏面，便可直接算出崩塌模態，進而得到塑性崩塌、增量崩塌與交替降伏，節省多餘的非矩陣的計算，以期未來能夠加入大型塑性程式分析。而此計算方法不論是桁架、梁或者是剛架，皆可套用此計算程序，為一個可靠的方法。

In design of civil structures, most regulatory codes have adopted limit design specifications; hence, the development of analysis methods --- limit analysis --- to match the limit design is a very important issue. A significant feature of plasticity is ``path to path", and the relationship between displacement and load is ``path-related". In general, there is an ``initial yield surface" before the material is first yielded. With the loading of the force, the material is switched to the plastic stage. With the different load paths, it will evolve into different sequences of subsequent yield surfaces; that is, the evolution of the yield surface is not unique and depends upon the paths. However, there exists a unique ``plastic limit surface" in the load space which demarcates the safe loads and the static collapses; that is to say, it is not necessary to carry out a complicated plastic time history analysis.

If the load is cyclically repeated, then plastic deformation either may result in vicious incremental collapse or alternating yield (plastic fatigue) phenomena, or may result in such appropriate residual stress distributions as shakedown phenomena occur. Between the safe cyclic loads and the incremental collapse or alternating yield, it is possible to establish a unique "shakedown limit surface" in the load space without the need for a complicated cyclic plastic time history analysis.

In this thesis, we discuss the calculation method of the plastic limit surface and the shakedown limit surface in the load space. By using the linearly elastic-perfectly plastic model, we construct the vector inequality and then extend the linear algebra calculation method to the inequality calculation. By skipping the calculation of the subsequent yield surfaces, we can directly calculate the collapse modes, and then obtain the plastic limit surface (static collapse) and the shakedown limit surface (incremental collapse and alternating yield). The developed calculation method, applicable to trusses, beams and rigid plane frames, is verified by examples taken from the existing literature.

摘要 (p.iii)
Abstract (p.v)
誌謝 (p.vii)
目錄 (p.ix)
使用符號與定義 (p.xix)
1 緒論 (p.1)
1.1 問題緣起 (p.1)
1.2 文獻回顧 (p.1)
1.3 極限理論 (p.2)
1.4 基本概念 (p.3)
1.5 本文架構 (p.5)
2 數學模型及推導 (p.7)
2.1 推導塑性極限面 (p.7)
2.1.1 殘餘應力 (p.9)
2.1.2 引理 Lemma (p.9)
2.1.3 使用全局化陣的目的 (p.10)
2.2 安定極限分析 (p.11)
2.2.1 增量崩塌 (p.11)
2.2.2 交替降伏 (p.15)
2.2.3 純彈性内力轉換陣的定義 (p.17)
2.2.4 增量崩塌面的處理方式 (p.17)
2.3 計算步驟 (p.20)
2.4 小結 (p.21)
3 桁架例題 (p.23)
3.1 桁架例題一 (p.23)
3.1.1 機動 力平衡 組成律 (p.24)
3.1.2 機動、力平衡與組成律的組合 (p.24)
3.1.3 極限面 (p.26)
3.2 桁架例題二 (p.29)
3.3 桁架例題三 (p.31)
3.3.1 塑性極限面——不對稱拉壓桿 (p.31)
3.3.2 塑性極限面——對稱拉壓桿 (p.34)
3.4 小結 (p.36)
4 構架例題 (p.37)
4.1 構架例題一 (p.37)
4.1.1 機動 (p.39)
4.1.2 力平衡 (p.40)
4.1.3 組成律 (p.41)
4.1.4 全局彈性勁度陣 (p.42)
4.1.5 塑性極限面一 (p.45)
4.2 構架例題二 (p.53)
4.2.1 塑性極限面二 (p.57)
4.2.2 安定極限面二之一 (p.61)
4.2.3 安定極限面二之二 (p.64)
4.3 構架例題三 (p.67)
4.3.1 機動 (p.69)
4.3.2 力平衡 (p.70)
4.3.3 全局彈性勁度陣 (p.71)
4.3.4 塑性極限面三之一 (p.73)
4.3.5 塑性極限面三之二 (p.80)
4.3.6 安定極限面三 (p.83)
4.4 構架例題四 (p.87)
4.4.1 機動 (p.90)
4.4.2 力平衡 (p.91)
4.4.3 組成律 (p.93)
4.4.4 全局彈性勁度陣 (p.95)
4.4.5 塑性極限面四之一 (p.99)
4.4.6 塑性極限面四之二 (p.110)
4.4.7 安定極限面四 (p.115)
4.5 構架例題五 (p.122)
4.5.1 塑性極限面五 (p.123)
4.5.2 機構 (p.138)
4.6 構架例題六 (p.139)
4.6.1 塑性極限面六 (p.139)
4.6.2 安定極限面六 (p.145)
4.7 構架例題七——不對稱塑性彎矩强度 (p.150)
4.8 小結 (p.152)
5 結論 (p.153)
參考文獻 (p.155)

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