2013
DOI: 10.1007/s00466-013-0853-8
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Local enrichment of the finite cell method for problems with material interfaces

Abstract: This paper proposes an efficient, hierarchical high-order enrichment approach for the finite cell method applied to problems of solid mechanics involving discontinuities and singularities. In contrast to the standard extended finite element method, where new degrees of freedom are introduced for all finite elements located in the enrichment zone, we define the enrichment on a so-called overlay mesh which is superimposed over the base mesh. The approximation on the base mesh is obtained by means of the finite c… Show more

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Cited by 71 publications
(64 citation statements)
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“…Instead of classical hierarchic shape functions [25] NURBS, which have become very popular thanks to the isogeometric analysis [10], can also be successfully used within the FCM, see [22,17]. Local refinement strategies have been also developed for the FCM and it turned out that the hp-d method [15,5] presents a general framework for local improvement of accuracy within the FCM, see [21,11].…”
Section: Introductionmentioning
confidence: 99%
“…Instead of classical hierarchic shape functions [25] NURBS, which have become very popular thanks to the isogeometric analysis [10], can also be successfully used within the FCM, see [22,17]. Local refinement strategies have been also developed for the FCM and it turned out that the hp-d method [15,5] presents a general framework for local improvement of accuracy within the FCM, see [21,11].…”
Section: Introductionmentioning
confidence: 99%
“…The continuous form is then obtained by performing either a low-or high-order interpolation, as φ(x) = n j=1 M j (x)Φ j . We showed in [5] that it is of advantage to employ Lagrange shape functions based on the Chen-Babuška points for M j since they yield superior interpolation properties with less error as compared to Lagrange shape functions defined on equidistant points. In addition to describing the location of the material interface, the level set function can be utilized to set up the enrichment function as F (x) = |φ(x)| [11].…”
Section: High-order Blended Enrichment Functionmentioning
confidence: 99%
“…In the case of the material interface, the exact solution exhibits a kink that cannot be represented by standard shape functions of the FCM if the interface is located within the element [5]. In order to overcome such a problem, several remedies have been proposed [5,7,13]. In [5], we showed that using the partition of unity method [1,8] together with the high-order representation of the material interface yields very accurate results, both in the displacements and the stresses.…”
Section: Introductionmentioning
confidence: 99%
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