用李群微分代數方法高精度計算彈塑性模型

Highly-accurate computation of elastoplastic models using Lie-group differential algebraic equations method

陳芳毅(Fang-Yi Chen)

指導教授 ： 劉進賢

國立臺灣大學/工學院/土木工程學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.02232

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Lie-group ； General linear group GL(n,R) ； Differential algebraic equations (DAEs) ； Yield-surface preserving scheme ； Lie-group differential algebraic equations (LGDAE) method

參考文獻

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