TY - JOUR
T1 - Analysis of elastic-plastic waves in a thin-walled tube by a novel lie-group differential algebraic equations method
AU - Liu, Chein Shan
AU - Atluri, Satya N.
N1 - Publisher Copyright:
Copyright © 2014 Tech Science Press.
PY - 2014
Y1 - 2014
N2 - In this paper, we adopt the viewpoint of a nonlinear complementarity problem (NCP) to derive an index-one differential algebraic equations (DAEs) system for the problem of elastic-plastic wave propagation in an elastic-plastic solid undergoing small deformations. This is achieved by recasting the pointwise complementary trio in the elastic-plastic constitutive equations into an algebraic equation through the Fischer-Burmeister NCP-function. Then, for an isotropicallyhardening/ softening material under prescribed impulse loadings on a thin-walled tube with combined axial-torsional stresses, we can develop a novel algorithm based on the Lie-group differential algebraic equations (LGDAE) method to iteratively solve the resultant DAEs at each time marching step, which converges very fast. The one-dimensional axial-torsional wave propagation problems under different imposed dynamical loading conditions and initial conditions are solved, to assess the performance of the LGDAE.
AB - In this paper, we adopt the viewpoint of a nonlinear complementarity problem (NCP) to derive an index-one differential algebraic equations (DAEs) system for the problem of elastic-plastic wave propagation in an elastic-plastic solid undergoing small deformations. This is achieved by recasting the pointwise complementary trio in the elastic-plastic constitutive equations into an algebraic equation through the Fischer-Burmeister NCP-function. Then, for an isotropicallyhardening/ softening material under prescribed impulse loadings on a thin-walled tube with combined axial-torsional stresses, we can develop a novel algorithm based on the Lie-group differential algebraic equations (LGDAE) method to iteratively solve the resultant DAEs at each time marching step, which converges very fast. The one-dimensional axial-torsional wave propagation problems under different imposed dynamical loading conditions and initial conditions are solved, to assess the performance of the LGDAE.
KW - Elastic-plastic wave
KW - Elastoplasticity
KW - Index-one differential algebraic equations
KW - Lie-group GL (n, double-struck R)
KW - Lie-group differential algebraic equations (LGDAE) method
UR - http://www.scopus.com/inward/record.url?scp=84907580335&partnerID=8YFLogxK
U2 - 10.3970/cmc.2014.041.001
DO - 10.3970/cmc.2014.041.001
M3 - Article
AN - SCOPUS:84907580335
SN - 1546-2218
VL - 41
SP - 1
EP - 36
JO - Computers, Materials and Continua
JF - Computers, Materials and Continua
IS - 1
ER -