Details

Autor(en) / Beteiligte

• Chin, Eric B.
• Sukumar, N.

Titel

Modeling curved interfaces without element‐partitioning in the extended finite element method

Ist Teil von

• International journal for numerical methods in engineering, 2019-11, Vol.120 (5), p.607-649

Ort / Verlag

Bognor Regis: Wiley Subscription Services, Inc

Erscheinungsjahr

2019

Link zum Volltext

Quelle

Wiley Online Library Journals Frontfile Complete

Beschreibungen/Notizen

• Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h‐refinement (p=1,2,…,5) and exponential rates of convergence with p‐refinement (p=1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian pth‐order spectral finite element meshes.