Torsional rigidity of a circular bar with multiple circular inclusions using the null-field integral approach |
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Authors: | Jeng-Tzong Chen Ying-Te Lee |
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Affiliation: | (1) Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan;(2) Department of Mechanical and Mechatronics Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan |
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Abstract: | In this article, a systematic approach is proposed to calculate the torsional rigidity and stress of a circular bar containing
multiple circular inclusions. To fully capture the circular geometries, the kernel function is expanded to the degenerate
form and the boundary density is expressed into Fourier series. The approach is seen as a semi-analytical manner since error
purely attributes to the truncation of Fourier series. By collocating the null-field point exactly on the real boundary and
matching the boundary condition, a linear algebraic system is obtained. Convergence study shows that only a few number of
Fourier series terms can yield acceptable results. Finally, torsion problems are revisited to check the validity of our method.
Not only the torsional rigidities but also the stresses of multiple inclusions are also obtained by using the present approach. |
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Keywords: | Torsional rigidity Null-field integral equation Degenerate kernel Fourier series Inclusion |
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