Open Access

ARTICLE

Analysis of Elastic-PlasticWaves in a Thin-Walled Tube By a Novel Lie-Group Differential Algebraic Equations Method

Chein-Shan Liu¹, Satya N. Atluri²

1 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan.E-mail: liucs@ntu.edu.tw
2 Center for Aerospace Research & Education, University of California, Irvine, USA.

Computers, Materials & Continua 2014, 41(1), 1-36. https://doi.org/10.3970/cmc.2014.041.001

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.

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Keywords

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