A multi-patch nonsingular isogeometric boundary element method using trimmed elements

Abstract

One of the major goals of isogeometric analysis is direct design-to-analysis, i.e., using computer-aided design (CAD) files for analysis without the need for mesh generation. One of the primary obstacles to achieving this goal is CAD models are based on surfaces, and not volumes. The boundary element method (BEM) circumvents this difficulty by directly working with the surfaces. The standard basis functions in CAD are trimmed nonuniform rational Bspline (NURBS). NURBS patches are the tensor product of one-dimensional NURBS, making the construction of arbitrary surfaces difficult. Trimmed NURBS use curves to trim away regions of the patch to obtain the desired shape. By coupling trimmed NURBS with a nonsingular BEM, the formulation proposed here comes close achieving the goal of direct design to analysis. Example calculations demonstrate its efficiency and accuracy.

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

“…IGABEM has thus been subsequently extended to many fields [68][69][70][71]. PU enriched IGABEM was later proposed in [72,73] and trimmed NURBS approaches were presented in [74,75]. Accelerated solutions were proposed in [42] and Galerkin version of IGABEM in [76,77] etc.…”

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

“…The abovementioned shape and topology optimization methods are based on the finite element method (FEM), some limitations of the FE approach include the disconnection between analysis and geometric models, low continuity between the elements and low efficiency of high-order elements. These limitations are successfully addressed by a new method called isogeometric analysis (IGA) [Hughes, Cottrell and Bazilevs (2005)], which directly uses the basis functions of a computer aided design (CAD) model as the shape functions of analysis model, IGA has since been used in a variety of domains [Benson, Bazilevs, Hsu et al (2011); Hsu and Bazilevs (2012); ; Wang, Benson and Nagy (2015); Yan, Deng, Korobenko et al (2017); Deng, Wu, Yang et al (2018)]. In the last decade, IGA has been adopted for both shape and topology optimizations, which provides several advantages over the established methods.…”

Stable isogeometric analysis of trimmed geometries

“…There are different approaches [20,21,33,39] which locally substitute the trimmed area by regular elements providing a mapping from the reference element where quadrature points are specified to the trimmed parameter space. In addition, tailored integration formulae may be used [26,38]. Due to their local nature, these concepts can be applied to complex CAGD models.…”