Differential-Algebraic Approach to Coupled Problems of Dynamic Thermoelasticity

WANG Lin-xiang; Roderick V. N. Melnik

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WANG Lin-xiang, Roderick V. N. Melnik. Differential-Algebraic Approach to Coupled Problems of Dynamic Thermoelasticity[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1036-1046.

Citation:

WANG Lin-xiang, Roderick V. N. Melnik. Differential-Algebraic Approach to Coupled Problems of Dynamic Thermoelasticity[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1036-1046.

Citation:

WANG Lin-xiang, Roderick V. N. Melnik. Differential-Algebraic Approach to Coupled Problems of Dynamic Thermoelasticity[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1036-1046.

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Differential-Algebraic Approach to Coupled Problems of Dynamic Thermoelasticity

WANG Lin-xiang¹,
Roderick V. N. Melnik²

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

Received Date: 2005-09-19
Rev Recd Date: 2006-06-17
Publish Date: 2006-09-15

Abstract

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 the 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 were 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.
- thermoelasticity,
- two-dimensional,
- differential-algebraic solvers

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References(24)

References

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