Abstract
SummaryThis paper presents the first method that enables the fully automatic generation of triangular meshes suitable for the so‐called non‐uniform rational B‐spline (NURBS)‐enhanced finite element method (NEFEM). The meshes generated with the proposed approach account for the computer‐aided design boundary representation of the domain given by NURBS curves. The characteristic element size is completely independent of the geometric complexity and of the presence of very small geometric features. The proposed strategy allows to circumvent the time‐consuming process of de‐featuring complex geometric models before a finite element mesh suitable for the analysis can be produced. A generalisation of the original definition of a NEFEM element is also proposed, enabling to treat more complicated elements with an edge defined by several NURBS curves or more than one edge defined by different NURBS. Three examples of increasing difficulty demonstrate the applicability of the proposed approach and illustrate the advantages compared with those of traditional finite element mesh generators. Finally, a simulation of an electromagnetic scattering problem is considered to show the applicability of the generated meshes for finite element analysis. ©2016 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
Highlights
High-order discretisation methods have gained an increased popularity during the last decade owing to the potential of providing higher accuracy with a reduced computational cost compared with traditional low-order methods [1,2,3,4,5]
This paper proposes a novel mesh generation technique that allows to produce triangular meshes where the elements account for the exact boundary representation of the domain irrespective of the desired element size and the geometrical complexity
The proposed strategy to compute interior integrals according to the new definition of a NEFEM element is to build a composite two-dimensional quadrature in elements affected by the non-uniform rational B-spline (NURBS) boundary representation of the domain
Summary
High-order discretisation methods have gained an increased popularity during the last decade owing to the potential of providing higher accuracy with a reduced computational cost compared with traditional low-order methods [1,2,3,4,5]. To fully exploit the potential advantages of high-order methods, very coarse curvilinear meshes and very high-order approximations are preferred, but as the size of the elements increases, the effect of geometric inaccuracies induced by the traditional polynomial approximation of curved boundaries inherent to the isoparametric formulation becomes evident. This paper proposes a novel mesh generation technique that allows to produce triangular meshes where the elements account for the exact boundary representation of the domain irrespective of the desired element size and the geometrical complexity. The meshes generated with this technique can produce elements where an edge contains corners of the boundary representation of the domain, enabling to encapsulate small and complex geometric features within coarse triangular elements.
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