An enhancement of overlapping finite elements

Lee, Sungkwon; Bathe, Klaus‐Jürgen

doi:10.1016/j.compstruc.2021.106704

Cited by 19 publications

(5 citation statements)

References 24 publications

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“…In future studies, the automatic procedure for adaptive enrichment could be extended to shell analysis [26][27][28][29][30][31], other physical problems [32][33][34][35][36][37], and other finite element methods like smoothed FEM [38]. It could also be applied to dynamic analysis, such as component mode synthesis (CMS) methods, to enhance the precision of dominant component modes through the adaptive application of cover functions [39][40][41].…”

Section: Discussionmentioning

confidence: 99%

A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme

et al. 2023

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This paper presents a novel and efficient solution procedure to improve 3D solid finite element analysis with an enrichment scheme. To this end, we employ finite elements enriched by polynomial cover functions, which can expand their solution space without requiring mesh refinement or additional nodes. To facilitate this solution procedure, an error estimation method and cover function selection scheme for 3D solid finite element analysis are developed. This enables the identification of nodes with suboptimal solution accuracy, allowing for the adaptive application of cover functions in a systematic and efficient manner. Furthermore, a significant advantage of this procedure is its consistency, achieved by excluding arbitrary coefficients from the formulations employed. The effectiveness of the proposed procedure is demonstrated through several numerical examples. In the majority of the examples, it is observed that the stress prediction error is reduced by more than half after applying the proposed procedure.

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Section: Discussionmentioning

confidence: 99%

A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme

et al. 2023

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“…The reference solution on which the errors are measured was obtained using a very fine mesh of 27-node elements. We see that using the AMORE mesh gives a significantly more accurate stress prediction than using the mesh of 8-node brick elements with incompatible modes [14].…”

Section: The Amore Schemementioning

confidence: 86%

“…For the triangular overlapping element considered in Figure 1 we have N = 3 but the formulation is very general. We have formulated in this way, two-dimensional triangular and quadrilateral elements, and three-dimensional tetrahedral, brick, pyramid, and prism elements [7][8][9][13][14][15].…”

Section: Overlapping Elementsmentioning

confidence: 99%

“…As an example, the distortion insensitivity compared to the use of traditional elements is displayed in the example solution of Figure 2 and Table 1. Here we compare the calculated response using a 4-node overlapping finite element (with a quadratic nodal polynomial) to the response predicted using the traditional 9-node element [14]. The 9-node element is quite powerful because it preserves its completeness when subjected to angular geometric distortions [1].…”

Section: Overlapping Elementsmentioning

confidence: 99%

“…While the overlapping elements clearly show specific strengths, a disadvantage of the elements is that they carry additional nodal degrees of freedom, since u K corresponds to a polynomial (or another suitable function). Hence the elements require a 1: Normalized y-direction displacement at the tip (x = 6, y = 0); for the normalization the reference displacement is −0.1081m [14]. higher order numerical integration in the evaluation of the stiffness and mass matrices than the traditional elements with the same number of nodes, and the bandwidth is larger in the assembled system matrices.…”

Section: Overlapping Elementsmentioning

confidence: 99%

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Modern Finite Element Analysis with AMORE

Bathe

Proceedings of the Fourteenth International Conference on Computational Structures Technology

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A major difficulty in traditional finite element analysis is the effort of meshing complex three-dimensional solids and structures. The inherent reason for the difficulty is that highly distorted elements should be avoided. This condition is difficult to satisfy because the traditional elements must abut to each other, that is, they cannot overlap. To overcome this restriction, we have developed "overlapping elements". These elements perform well even when highly distorted and hence can be used much more easily in meshing a complex domain. However, they use additional nodal degrees of freedom which add to the computational effort of solution. To reduce the overall solution cost, including the meshing, we focus on the AMORE scheme in which traditional undistorted elements are used to discretize most of the analysis domain and overlapping elements are used for the rest of the domain. The premise is that in this way, the meshing effort is much reduced and the computational effort is also less than in a traditional finite element analysis. This way the use of AMORE leads to an overall efficient modern finite element analysis.

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