The semi-analytical evaluation for nearly singular integrals in isogeometric elasticity boundary element method.

*(English)*Zbl 1403.65199Summary: Benefiting from improvement of accuracy in modeling complex geometry and integrity of discretization and simulation, the isogeometric analysis in the boundary element method (IGABEM) has now been implemented by several groups. However, the difficulty of evaluating the nearly singular integral in IGABEM for elasticity has not yet been effectively solved, which will hinder the application of IGABEM in engineering structure analysis. Herein, the nearly singular integrals in IGABEM are separated to the non-singular part and singular part by the subtraction technique. The integral kernels in singular part are approximated by the Taylor series polynomial expressions, in which different orders of derivatives are interpolated by the non-uniform rational B-splines (NURBS). Furthermore, the analytical formulations for the singular part with the approximated kernels are derived by a series of integration by parts, while the non-singular part is calculated with Gaussian quadrature. In this way, a semi-analytical method is proposed for the nearly singular integrals in the IGABEM. Comparing with the conventional IGABEM, the present method can yield accurate displacement and stress for inner points much closer to the boundary. It can obtain effective results with fewer elements than the finite element method because of the precise simulation of geometry and boundary-only discretization.

##### MSC:

65N38 | Boundary element methods for boundary value problems involving PDEs |

65D30 | Numerical integration |

##### Software:

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\textit{Z. Han} et al., Eng. Anal. Bound. Elem. 95, 286--296 (2018; Zbl 1403.65199)

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