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研究生:李嶸杉
研究生(外文):R. S. Li
論文名稱:基於主對偶法之連續式極限分析
論文名稱(外文):Sequential Limit Analysis by a Primal-dual Method
指導教授:呂學育
指導教授(外文):S. Y. Leu
口試委員:廖國基藍庭顯
口試委員(外文):Kuo-Chi LiaoTing-Hsien Lan
口試日期:2012-07-17
學位類別:碩士
校院名稱:中華科技大學
系所名稱:飛機系統工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:57
中文關鍵詞:極限分析連續式極限分析主對偶法混合式硬化有限元素法
外文關鍵詞:Limit analysisSequential limit analysisPrimal-dual methodCombined hardeningFinite-element method
相關次數:
  • 被引用被引用:0
  • 點閱點閱:142
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  • 下載下載:10
  • 收藏至我的研究室書目清單書目收藏:0
極限分析基於下限或上限定理,可直接估算結構的塑性極限承載能力。另一方面,連續式極限分析藉由降伏強度及結構變形幾何的漸次迭代更新,可應用於求解考慮應變硬化性質的極限承載能力。基於主對偶法的極限分析,利用下限與上限問題陳述的對偶性質,可同時計算下限及上限解。本研究探討主對偶法在連續式極限分析的應用,用於求解考慮應變硬化性質的極限載重與失效模式。在文中我們考慮構架的極限分析問題,毋需猜測其可能之失效模式,直接由構件的力平衡條件,而推導其主對偶法所需之數學規劃模式,並探討邊界條件對構架的極限載重與失效模式之影響。此外,我們也考慮具混合式硬化性質的桁架結構之連續式極限分析問題,同時掌握桁架結構的極限載重與各接點之位移資料,主要探討材料硬化性質對桁架結構的極限載重之影響。最後,由構架與桁架分析案例之結果顯示,本文基於主對偶方法的極限分析或連續式極限分析結果,與文獻上或有限元素彈塑性分析結果比較均具有良好吻合度。
Limit analysis is a direct method to provide plastic limit load by the lower bound or upper bound theorem. By sequential limit analysis, it is to conduct a sequence of limit analysis problems with updating the yield criterion and the deformed configuration. The duality relationship between the static and the kinematic formulations can be applied to improve the numerical investigation of limit analysis. It calculates the primal-dual optimal solution. The paper is aimed to study the load bearing capacity of strain-hardening structures by using sequential limit analysis based on a primal-dual method. Illustrative examples are focused on framed and truss structures. The primal-dual interior-point algorithm is adopted and incorporated with the concept of sequential limit analysis and compared to the results obtained by the finite-element elastic-plastic analysis. Good agreement has demonstrated the accuracy of sequential limit analysis based on a primal-dual method.
誌謝 i
摘要 ii
ABSTRACT iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
第一節 前言 1
第二節 研究動機及目的 2
第三節 研究方法 2
第四節 論文架構 3
第二章 文獻回顧與理論探討 4
第一節 文獻回顧 4
第二節 理論探討 5
第三章 構架結構極限分析 10
第一節 前言 10
第二節 問題陳述 10
第三節 數學模式建立 11
壹、 單層門式構架結構 11
貳、 雙層門式構架結構 16
第四節 分析結果與討論 21
壹、 單層門式構架結構 22
貳、 雙層門式構架結構 23
第四章 桁架結構連續式極限分析 35
第一節 前言 35
第二節 問題陳述 35
第三節 數學模式建立 36
壹、 三桿件桁架結構 36
貳、 橋樑式桁架結構 36
第四節 分析結果與討論 38
壹、 三桿件桁架結構 38
貳、 橋樑式桁架結構 40
第五章 結論與未來展望 51
第一節 結論 51
第二節 未來展望 52
參考文獻 53

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