工學院: 土木工程學研究所指導教授: 劉進賢陳芳毅Chen, Fang-YiFang-YiChen2017-03-132018-07-092017-03-132018-07-092015http://ntur.lib.ntu.edu.tw//handle/246246/277988本論文分別針對廣義彈塑性模式 (完全彈塑性模式、線性走動硬軟化模式、非線性走動硬軟化模式) 與材料彈塑性模式 (Prandtl-Reuss 模式、Prager 走動硬軟化模式、Armstrong-Frederick 走動硬軟化模式) 採納非線性互補問題 (NCP) 形式 [A. Fischer, Solution of monotone complementarity problems with locally Lipschitzian functions, Mathematical Programming, Volume 76, Issue 3 (1997) 513-532.] 改寫其互補三元為一代數方程式，使上述彈塑性模式之數學形式由「微分代數方程組」和「不等式」改為微分代數方程組 (DAEs) 。為了求解彈塑性模式，本文建構彈塑性模式之李群 (廣義線性群 GL(n,R)) 微分代數方程組算法 [C. S. Liu, Elastoplastic models and oscillators solved by a Lie-group differential algebraic equations method, Int. J. Non-Linear Mech. 69 (2015) 93-108.] ，並且評估此算法在上述六個模式的效率與準確性。In this thesis, the complementary trios of the generalized elastoplastic models (the perfectly elastoplastic model, the elastoplastic model with linearly kinematic hardening, the elastoplastic model with non-linearly kinematic hardening) and the material elastoplastic models (the Prandtl-Reuss model, the materical model with Prager hardening rules, the materical model with Armstrong-Frederick hardening rules) have been transformed into the algebraic equations according to the formulation of nonlinear complementarity problem (NCP). [A. Fischer, Solution of monotone complementarity problems with locally Lipschitzian functions, Mathematical Programming, Volume 76, Issue 3 (1997) 513-532.] Thus, the mathematical formulation of elastoplastic models which are combination of “differential algebraic equations” and “inequalities” are changed to the differential algebraic equations (DAEs). In order to solve the elastoplastic models, we have constructed the Lie group (generalized linear group GL(n, R)) differential algebraic equations method [C. S. Liu, Elastoplastic models and oscillators solved by a Lie-group differential algebraic equations method, Int. J. Non-Linear Mech. 69 (2015) 93-108.] for the six elastoplastic models and have assess efficiency and accuracy of the scheme.4484033 bytesapplication/pdf論文公開時間: 2015/7/23論文使用權限: 同意有償授權(權利金給回饋學校)李群廣義線性群微分代數方法保降伏面法李群微分代數方程法Lie-groupGeneral linear group GL(n,R)Differential algebraic equations (DAEs)Yield-surface preserving schemeLie-group differential algebraic equations (LGDAE) methodthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/277988/1/ntu-104-R02521249-1.pdf