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

Chein-Shan Liu1, Satya N. Atluri2
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan.E-mail: liucs@ntu.edu.tw
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.

Keywords

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

Cite This Article

C. . Liu and S. N. . Atluri, "Analysis of elastic-plasticwaves in a thin-walled tube by a novel lie-group differential algebraic equations method," Computers, Materials & Continua, vol. 41, no.1, pp. 1–36, 2014.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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