Highly-accurate computation of elastoplastic models using Lie-group differential algebraic equations method
Date Issued
2015
Date
2015
Author(s)
Chen, Fang-Yi
Abstract
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.
Subjects
Lie-group
General linear group GL(n,R)
Differential algebraic equations (DAEs)
Yield-surface preserving scheme
Lie-group differential algebraic equations (LGDAE) method
Type
thesis
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