洪宏基臺灣大學：土木工程學研究所許福鑫Hsu, Fu-HsinFu-HsinHsu2007-11-252018-07-092007-11-252018-07-092007http://ntur.lib.ntu.edu.tw//handle/246246/50469本文利用片段線性模式(piecewise-linear model)與包絡面定理(envelope theorem)及非線性規劃(nonlinear programming),推導出線性走動硬軟化模式、等向性硬軟化模式、混合硬軟化模式、二次異向性混合硬軟化模式。 本文探討長久以來利用實驗數據建構彈塑組成律,會不具有簡單性、廣義性的問題。首創嘗試將組成模式作無窮維分解、有限維近似,以簡單廣義的片段線性模式反過來建構彈塑性組成演化模式,突破傳統利用實驗數據建構彈塑組成律的方法。模式本身對材料並沒有限制,相當具有廣義性,除了降伏式要為凸(convex),無論為等向性、異向性材料、硬軟化材料...等,皆可以成功建構。不僅適用於材料,更可以運用在一般結構、構件...等 彈塑行為描述上。 最後以上述四個模式,給三組不同的應力控制路徑,作數值實例,確定可以執行。並且模擬的結果,能反映與部分實驗觀察趨勢,尤其一般認為相當難描述的變形引致異向性現象。In this thesis, we study the evolution of elastoplastic internal variables by using piecewise-linear models, the envelope theorem and nonlinear programming to derive linear kinematic hardening-softening model,isotropic hardening-softening model, mixed hardeing-softening model and quadratic anisotropy mixed hardening-softening model. Phenomenological approaches to constructing elastoplastic constitutive laws by experiments are considered for a long to be lack of simplicity and generality.The first time we attempt trying to decompose the constitutive models into infinite dimensions and approximate them in finite dimensions, and conversely use simple and general piecewise-linear models to build up the constitutive models. The models have no restrictions except that the yield functions need to be convex. Isotropic or anisotropic and hardeing or softening materials can be constructed successfully.The models are written in forms capable of describing the behavior of elastoplasticity of not only materials but also common structures and members. To make sure they can be excuted, we give four examples for the above-mentioned models, subject to three different stress controlled paths.The results show that the model do reflect part of experimental trends, especially the very difficultly described phenomenon of deformation induced anisotropy.目錄 誌謝...............................一 摘要...............................二 目錄...............................三 表目錄.............................五 圖目錄.............................六 附錄...............................七 第一章 導論.................................3 1.1 前言語文獻回顧...........................3 1.2 研究目的.................................4 1.3 研究方法.................................5 第二章 彈塑性組成模式.......................7 2.1 片段線性模式-有限個降伏平面..............7 2.2 線性走動硬軟化組成模式...................9 2.3 等向性硬軟化組成模式....................13 2.4 混合硬軟化組成模式......................15 2.5 二次異向性混合硬軟化組成模式............18 第三章 數值實例.............................21 例一 走動硬軟化組成模式實例.................21 例二 等向性硬軟化組成模式實例...............22 例三 混合硬軟化組成模式實例.................22 例四 二次異向性硬軟化組成模式實例...........22 第四章 結論與建議...........................23 參考文獻....................................241038684 bytesapplication/pdfen-US片段線性包絡面非線性規劃彈塑組成律變形引致異向性。piece-wise linearenvelopenonlinear programmingelastoplastic constitutive lawsdeformation induced anisotropythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/50469/1/ntu-96-R94521240-1.pdf