Abstract
This work presents some numerical aspects of isogeometric boundary element methods (IGABEM). The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface. Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis. Then a numerical implementation of IGABEM on the trimmed NURBS is detailed. Based on this idea, the surface crack problem is modeled incorporation with the phantom element method. The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.
Highlights
The isogeometric analysis (IGA) uses the spline-basis functions, which are adopted to describe CAD geometry, to approximate the physical fields in analysis
The corporation of the IGA and boundary element methods (BEM) provides a direct link between CAD and analysis since both methodologies are related to the boundary representation of the body
Several numerical aspects, such as the singular integration, trimmed NURBS and surface crack modeling, of the IGABEM are investigated in detail
Summary
The isogeometric analysis (IGA) uses the spline-basis functions, which are adopted to describe CAD geometry, to approximate the physical fields in analysis. Within the BEM community, Beer et al [5] proposed a double mapping method to perform the integration on NURBS This method relies on the establishment of the mapping area and is not able to be applied directly for a closed trimming curve, but later they proposed a stable extended B-splines scheme for IGABEM with trimmed geometry [14]. The surface crack problem has two manifolds in numerical implementation: one is the coinciding crack surfaces inside the body domain, the other is the surface discontinuity along the geometry boundary The latter can be considered as a problem of cracks in 2D plane or 3D shell conditions in the finite element method (FEM).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
