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Differential-algebraic approach to coupled problems of dynamic thermoelasticity

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Abstract

An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.

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Authors and Affiliations

  1. MCI, Faculty of Science and Engineering, University of Southern Denmark, Sonderborg, DK-6400, Denmark

    Wang Lin-xiang Doctor (Associate Professor)

  2. Center for Coupled Dynamics & Complex Systems, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, Canada, N2L 3C5

    Roderick V. N. Melnik

Authors
  1. Wang Lin-xiang Doctor
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  2. Roderick V. N. Melnik
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Correspondence to Wang Lin-xiang Doctor.

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Communicated by ZHOU Zhe-wei

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Wang, Lx., Melnik, R.V.N. Differential-algebraic approach to coupled problems of dynamic thermoelasticity. Appl Math Mech 27, 1185–1196 (2006). https://doi.org/10.1007/s10483-006-0905-z

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  • DOI: https://doi.org/10.1007/s10483-006-0905-z

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2000 Mathematics Subject Classification

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