@Article{cmc.2014.041.001, AUTHOR = {Chein-Shan Liu, Satya N. Atluri}, TITLE = {Analysis of Elastic-PlasticWaves in a Thin-Walled Tube By a Novel Lie-Group Differential Algebraic Equations Method}, JOURNAL = {Computers, Materials \& Continua}, VOLUME = {41}, YEAR = {2014}, NUMBER = {1}, PAGES = {1--36}, URL = {http://www.techscience.com/cmc/v41n1/22742}, ISSN = {1546-2226}, ABSTRACT = {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.}, DOI = {10.3970/cmc.2014.041.001} }