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. 2016 May;7(3):445-52.
doi: 10.1016/j.jare.2016.03.004. Epub 2016 Mar 14.

Analysis of thin plates with holes by using exact geometrical representation within XFEM

Logah Perumal  1 , C P Tso  1 , Lim Thong Leng  1
Affiliations

Analysis of thin plates with holes by using exact geometrical representation within XFEM

Logah Perumal et al. J Adv Res. 2016 May.

Abstract

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

Keywords: Exact geometrical representation; Numerical and exact integration; Quadrature rules; Thin plates with holes; XFEM.

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Figures

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Graphical abstract
Fig. 1
Fig. 1
(a) Meshing in conventional FEM. (b) Meshing in XFEM. (c) Enriched elements and enriched nodes in XFEM.
Fig. 2
Fig. 2
Sub-division of element 17 into 5 quadrilaterals for numerical integration.
Fig. 3
Fig. 3
Example of a domain with linear and curved sides in two dimensions. (a) Without partitioning. (b) Partitioned domain.
Fig. 4
Fig. 4
12 possible combinations for the circular curve within the enriched elements (a) combinations 1a to 6a and (b) combinations 1b to 6b.
Fig. 5
Fig. 5
L2 errors for case 1 by utilizing numerical integration technique (a) L2 errors for mesh level 4 by 4, with 25 global nodes (b) L2 errors for mesh level 8 by 8, with 81 global nodes.
Fig. 6
Fig. 6
Comparison of L2 errors between the classical integration technique and the proposed technique, by using fifth order numerical integration.
Fig. 7
Fig. 7
Geometry of the problem domain (a) Plate with curved (polynomial curves) hole without mesh and (b) 4 by 4 mesh level for the problem domain.
None
See this image and copyright information in PMC

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