TY - JOUR
T1 - Evaluation of Singular and Nearly Singular Integrals in the BEM with Exact Geometrical Representation
AU - Yaoming Zhang, Wenzhen Qu & Yan Gu
JO - Journal of Computational Mathematics
VL - 4
SP - 355
EP - 369
PY - 2013
DA - 2013/08
SN - 31
DO - http://doi.org/10.4208/jcm.1301-m4021
UR - https://global-sci.org/intro/article_detail/jcm/9740.html
KW - BEM, Singular integrals, Nearly singular integrals, Boundary layer effect, Thin
walled structures, Exact geometrical representation.
AB - <p style="text-align: justify;">The geometries of many problems of practical interest are created from circular or elliptic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations (BIEs) and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular properties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occurring in the boundary element method (BEM) for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.</p>