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研究生:李璟鑫
研究生(外文):Jing-Shin Li
論文名稱:基於主對偶法之彈性安定分析
論文名稱(外文):Shakedown Analysis Based on a Primal-Dual Method
指導教授:呂學育
指導教授(外文):Shyue-Yuh 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:2014-06-26
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:2014
畢業學年度:102
語文別:中文
論文頁數:75
中文關鍵詞:安定分析主對偶法強對偶數學規劃最佳化演算有限元素法
外文關鍵詞:Shakedown analysisPrimal-dual methodStrong dualityMathematical programmingOptimization algorithmFinite element method
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  • 被引用被引用:2
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本論文主要為基於主對偶法,針對承受循環式負載之彈塑性結構進行安定分析的探討。安定分析為一種直接法,能夠直接求取結構承受循環式負載時之彈性安定負載,因此安定分析可視為結構設計及安定評估的有力工具。基於安定分析的下限定理及上限定理,我們可將求解安定負載的問題陳述為最佳化問題。本研究除了利用解析方式驗證存在於下限問題陳述與上限問題陳述間的強對偶關係,並採用數值方式證實最大下限解等於最小上限解之強對偶關係。最後,藉由主對偶演算法同時求得主變數及對偶變數。在分析案例中,採用構架結構與桁架結構作為安定分析之問題探討,並利用MATLAB之最佳化工具箱進行安定負載問題的最佳解演算。由分析案例之結果顯示,基於最佳化之演算結果與有限元素彈塑性分析軟體ABAQUS分析結果比對吻合度良好。
The thesis aims to investigate shakedown analysis of framed structures and truss structures by a primal-dual method. Shakedown analysis is a direct method to evaluate the load carrying capacity of a structure subjected to variable cyclic loads. The direct method is an effective tool for structure optimal design and safety evaluation. By the static or kinematic shakedown theorem, we can formulate the shakedown analysis problem as an optimization problem. In the thesis, we illustrate the duality relationship between the lower and upper bound formulations analytically by the Hölder inequality and numerically by the primal and dual analysis, respectively. Accordingly we can solve simultaneously lower bound problem and upper bound problem by a primal-dual method. The primal-dual algorithm provided by MATLAB is adopted to perform the shakedown analysis of framed structures and truss structures, respectively. For comparisons and validations, elastic-plastic analysis is also conducted by the commercial finite-element code ABAQUS. Finally, comparisons with good agreement validate the numerical results presented in the paper.
致謝 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 3
第四節 論文架構 3
第二章 文獻回顧及理論探討 6
第一節 文獻回顧 6
第二節 理論探討 7
第三章 構架結構之安定分析 15
第一節 前言 15
第二節 問題陳述 15
第三節 數學模式建立 16
第四節 分析結果及討論 18
第四章 桁架結構之安定分析 30
第一節 前言 30
第二節 問題陳述 30
第三節 數學模式建立 31
第四節 分析結果及討論 35
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
附錄一
附錄二
附錄三

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