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

• Main Authors: Fang-Yi Chen, 陳芳毅
• Other Authors: 劉進賢
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/16798727967143146144

碩士 === 國立臺灣大學 === 土木工程學研究所 === 103 === 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.