Isogeometric boundary element analysis based on UE-splines

Abstract

UE-splines are generalizations of uniform polynomial splines, trigonometric splines, hyperbolic splines and exponential splines defined as parametric splines in non-rational form. At the same time, they can exactly represent a wide class of basic analytic shapes commonly used in engineering applications. Further, UE-splines with uniform knot intervals can be conveniently generated by subdivision methods. In this paper, we use them to model many kinds of basic analytic shapes and generate circular splines interpolating points and tangents, and then conduct isogeometric boundary element analysis (IGABEM) of models defined by UE-splines. Taking 2D elasticity problems as an example, we describe a frame and technologies of IGABEM based on UE-splines, including relevant formulation, refinement based on UE-spline subdivision method and optimal post-processing. We develop traction recovery method for computing boundary stress to avoid strong singular integral problem, and adopt a divide-and-conquer strategy to obtain distribution nephograms with clear boundary for all kinds of physical items. A set of numerical experiments demonstrates that UE-splines have many merits on both modeling and solving IGABEM problems.