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| A novel semi-analytic algorithm of nearly singular integrals in high order boundary element analysis of 2D potential |
| Received:August 26, 2013 Revised:December 14, 2013 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201406013 |
| KeyWord:potential BEM high order element nearly singular integrals semi-analytic method |
| Author | Institution |
| 胡宗军 |
合肥工业大学 土木与水利工程学院, 合肥 |
| 牛忠荣 |
合肥工业大学 土木与水利工程学院, 合肥 |
| 程长征 |
合肥工业大学 土木与水利工程学院, 合肥 |
| 周焕林 |
合肥工业大学 土木与水利工程学院, 合肥 |
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| Abstract: |
| The evaluation of the nearly singular integrals on general high order element is presently one of the difficulties in boundary element method (BEM).In this paper,the geometric feature of the high order elements in two dimensional (2D) BEM is expressed by the local coordinate,in which the relative distance from a source point to high order element (named approach degree) is defined.Then,the approximate kernel functions of the nearly singular integrals are constructed for 3-noded quadratic isoparametric element in 2D potential BEM,which have the same singularity as the kernel functions of the element integrals.By subtracting the approximate kernel functions from the singular kernels on the nearly singular integral elements,the original nearly singular integral is divided into two parts,one is regular integral and the other is the nearly singular integral.The former can be calculated accurately by Gauss numerical quadrature.The later can be calculated by the analytic formulation established in the paper.Thus the novel semi-analytic algorithm is proposed to evaluate the nearly strongly singular and hyper-singular integrals on the high order elements in 2D potential BEM.Finally,two examples are given to demonstrate the present algorithm is efficient and accurate for treating the nearly singular integrals on the high order elements. |
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