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The Lie-Group Shooting Method for Thermal Stress Evaluation Through an Internal Temperature Measurement

Chein-Shan Liu1

Department of Mechanical & Mechatronic Engineering and Department of Harbor & River Engineering, Taiwan Ocean University, Keelung, Taiwan. E-mail:

Computers, Materials & Continua 2008, 8(1), 1-16.


In the present work we study numerical computations of inverse thermal stress problems. The unknown boundary conditions of an elastically deformable heat conducting rod are not given a priori and are not allowed to measure directly, because the boundary may be not accessible to measure. However, an internal measurement of temperature is available. We treat this inverse problem by using a semi-discretization technique, of which the time domain is divided into many sub-intervals and the physical quantities are discretized at these node points of discrete times. Then the resulting ordinary differential equations in the discretized space are numerically integrated towards the spatial direction by the Lie-group shooting method to find unknown boundary conditions. The key point is based on one-step Lie group elements: G(r) = G(y0,yl). We are able to search missing boundary conditions through a minimum discrepancy from the targets in terms of a weighting factor r ∈ (0,1). Several numerical examples were worked out to persuade that this novel approach has good efficiency and accuracy. Although the measured temperature is disturbed by large noise, the Lie group shooting method is stable to recover the boundary conditions very well.


Cite This Article

C. Liu, "The lie-group shooting method for thermal stress evaluation through an internal temperature measurement," Computers, Materials & Continua, vol. 8, no.1, pp. 1–16, 2008.

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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