臺灣博碩士論文加值系統

安定分析能夠簡便地求取結構承受循環負載時之承載能力，因此可將此分析方法視為結構設計及安定評估的有力工具。本論文探討桁架結構承受循環負載作用時，基於上限、下限定理進行結構安定分析。我們將上下限問題陳述為最佳化問題，並藉由最佳化理論與對偶定理，可獲得最大下限解等於最小上限解，即為安定分析之真正解。
本文利用數值運算軟體MATLAB所提供最佳化工具箱撰寫程式碼進行安定負載之最佳解演算，另一方面，藉由ABAQUS所提供之逐步分析法，驗證MATLAB所計算之安定負載之最佳解，另外探討當桁架結構超出安定極限負載時，可能發生塑性崩潰、低週期疲勞破壞、棘輪等幾種彈塑性行為，並利用應力與應變關係圖、塑性耗散來判斷整體結構所發生彈塑性行為。於案例分析中，探討對稱與非對稱之桁架結構進行安定分析之問題探討，考慮阿姆斯特朗-弗雷德里克(AF)、Chaboche走動式硬化性質。最後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分析軟體ABAQUS所得到結果比對吻合度良好。

This thesis investigates elastic shakedown limit loads and elastic-plastic analysis of structures subjected to cyclic loads made of nonlinear kinematic hardening materials. In the thesis, the step-by-step analysis of the computer code ABAQUS is applied to consider elastic-perfectly plastic and kinematic hardening materials, respectively. Parametric studies are made to study the prediction of shakedown limit loads and the relationship between shakedown limit loads and plastic limit loads. Also, validations and comparisons are made between the results obtained by ABAQUS and MATLAB. Moreover, Armstrong-Frederick kinematic hardening model is utilized in the related parametric studies

誌謝 I
摘要 II
目錄 IV
表目錄 V
圖目錄 V
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
第三章 對稱三桿件桁架之循環彈塑性行為分析 9
第一節 前言 9
第二節 問題描述 9
第三節 數值分析模式建立 10
第四節 分析結果與討論 10
第五節 結論 18
第四章 非對稱三桿件桁架之循環彈塑性行為分析 30
第一節 前言 30
第二節 問題描述 30
第三節 數值分析模式建立 31
第四節 分析結果與討論 31
第五節 結論 40
第五章 結論與未來展望 52
第一節 結論 52
第二節 未來展望 53
參考文獻 54
作者簡介 56

[1]李璟鑫，基於主對偶法之彈性安定分析，碩士論文，中華科技大學，中華民國 103年 6月
[2]J. A. König and G. Maier, “Shakedown analysis of elastic-plastic structures: a review of recent developments,” Nuclear Engineering and Design, Vol.66, pp.81-95, 1981.
[3]J. A. König, “Shakedown of elastic-plastic structure,” Nuclear Engineering and Design, Vol.28, pp.121-136, 1987.
[4]D. Weichert and G. Maier, “Inelastic behavior of structures under variable repeated loads: direct analysis methods,” New York, Springer, 2002.
[5]M. Staat and M. Heitzer, “Numerical methods for limit and shakedown analysis:deterministic and probabilistic problems,” John von Neumann Institute for Computing, 2003.
[6]D. Weichert and A. Ponter, “Limit states of materials and structures: Direct Methods,” New York, Springer, 2009.
[7]S.-Y.Leu, J.-S.Li “Shakedown analysis of truss structures with nonlinear
kinematic hardening,” International Journal of Mechanical Sciences Vol.103, pp.172-180, 2015.
[8]P. Segle, G. Eklund, and M. Skog, “A two-rod testing approach for understanding ratcheting in structures, ” International Journal of Pressure Vessels
and Piping, Vol.139-140, pp.184-193, 2016
[9]R. Hill, “The mathematical theory of plasticity,” Oxford, Clarendon Press, 1950.
[10]S. Bari and T. Hassan, “Anatomy of coupled constitutive models for ratcheting simulation,” International Journal of Plasticity, Vol.16, pp.381-409,
2000.
[11]P. J. Armstrong and C. O. Frederick, “A mathematical representation of the multiaxial bauschinger effect”, Materials at High Temperatures,Vol.27,
pp.1-26, 1966.
[12]J. L. Chaboche, “Time-independent constitutive theories for cyclic plasticity,” International Journal of Plasticity. Vol. 2, pp.149-188, 1986.
[13]J. L. Chaboche, K. Dang-Van, and G. Cordier, “Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel,” Proceeding of the 5th International Conference on SMiRT, Germany, 1979
[14]A. H. Mahmoudi, S. M. Pezeshki-Najafabadi and H. Badnava “Parameter
determination of Chaboche kinematic hardening model using a multi objective Genetic Algorithm, ”Computational Materials Science, Vol.50, pp.1114-1122,
2011.
[15]O. U. Colak, “Kinematic hardening rules for modeling uniaxial and multiaxal ratcheting,” Materials & Design, Vol.29, pp.1575-1581, 2008.
[16]M. Rezaiee-Pajand and S. Sinaie, “On the calibration of the Chaboche
hardening model and a modified hardening rule for uniaxial ratcheting
prediction,” International Journal of Solids and Structures, Vol.46, pp.3009-3017, 2009.
[17]MATLAB.
http://www.mathworks.com/help/optim/ug/linprog.html, 2016/06/07
[18]MATLAB.
http://www.mathworks.com/help/optim/ug/fmincon.html, 2016/06/07
[19]ABAQUS, ABAQUS Analysis User’s Manual, Dassault Systemes Simulia Corp. Providence, RI, USA.