Analysis of elastic-plastic waves in a thin-walled tube by a novel lie-group differential algebraic equations method

Chein Shan Liu, Satya N. Atluri

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalComputers, Materials and Continua
Volume41
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Elastic-plastic wave
  • Elastoplasticity
  • Index-one differential algebraic equations
  • Lie-group GL (n, double-struck R)
  • Lie-group differential algebraic equations (LGDAE) method

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