HU Zong-jun, NIU Zhong-rong, CHENG Chang-zheng, ZHOU Huan-lin. High-Order Boundary Element Analysis of Temperature Fields in Thin-Walled Structures[J]. Applied Mathematics and Mechanics, 2015, 36(2): 149-158. doi: 10.3879/j.issn.1000-0887.2015.02.004
 Citation: HU Zong-jun, NIU Zhong-rong, CHENG Chang-zheng, ZHOU Huan-lin. High-Order Boundary Element Analysis of Temperature Fields in Thin-Walled Structures[J]. Applied Mathematics and Mechanics, 2015, 36(2): 149-158.

# High-Order Boundary Element Analysis of Temperature Fields in Thin-Walled Structures

##### doi: 10.3879/j.issn.1000-0887.2015.02.004
Funds:  The National Natural Science Foundation of China(11272111;11372094)
• Rev Recd Date: 2014-11-10
• Publish Date: 2015-02-15
• The geometric features of 3-node elements in the 2D BEM were analyzed, and the relative distance (namely the approach degree) from a source point to a high-order element was defined. Based on the geometric features, the approximate kernel functions were constructed with the same II-type singularity as the nearly singular kernel functions. For the nearly singular integrals, the dominant singular parts were separated from the original kernel functions through subtraction. After subtraction of the approximate kernel functions, the original kernel functions were rid of near singularity and turned into the sum of two integrals, of which one was a regular integral to be evaluated accurately with the conventional Gaussian quadrature, the other was a singular integral to be calculated with a series of analytical formulae derived herein. Then a new semi-analytical algorithm was established to compute the nearly singular integrals for the high-order elements effectively. In verification, the new method was applied to calculate several temperature field examples of thin-body structures for 2D potential boundary element analysis. The results indicate that the presented high-order-element semi-analytic algorithm takes full advantage of the BEM and has highly improved calculation accuracy and efficiency.
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