TY - EJOU
AU - Liu, Chein-Shan
AU - Atluri, Satya N.
TI - Analysis of Elastic-PlasticWaves in a Thin-Walled Tube By a Novel Lie-Group Differential Algebraic Equations Method
T2 - Computers, Materials \& Continua
PY - 2014
VL - 41
IS - 1
SN - 1546-2226
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 - Elastoplasticity
KW - Lie-group GL(n
KW - R)
KW - Index-one differential algebraic equations
KW - Elastic-plastic wave
KW - Lie-group differential algebraic equations (LGDAE) method
DO - 10.3970/cmc.2014.041.001