Efficient Analysis of Discontinuous Elements Using a Modified Selective Enrichment Technique

Semin Lee; Taehun Kang; Hayoung Chung

doi:10.7734/COSEIK.2022.35.5.267

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2022 Vol.35, Issue 5 Preview Page Next Page

Research Paper

Efficient Analysis of Discontinuous Elements Using a Modified Selective Enrichment Technique 수정된 선택적 확장 기법을 이용한 불연속 요소의 효율적 해석

31 October 2022. pp. 267-275

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Abstract

Using a nonconforming mesh in enrichment methods results in several numerical issues induced by discontinuities and singularities found within the solution spaces, including the computational overhead during integration. In this study, we present a novel enrichment technique based on the selective expansion technique of moment fitting (Düster and Allix, 2020). In particular, two modifications are proposed to address the inefficiency during the integration process. First, a feedforward artificial neural network is introduced to correlate the implicit functions and integration moments. Through numerical examples, it is shown that the efficiency of the method is greatly improved when compared with existing expansion techniques, whereas the solution accuracy is maintained. Additionally, the finite element and domain representation grids are separated, which in turn improves the solution accuracy even for coarse mesh conditions.

Keywords

moment fitting method

artificial neural network

adaptive integration

level set function

Non-conforming mesh를 이용해 구조적인 불연속성을 해석 시 요소 내 함수 불연속성과 특이점이 존재하며, 이로 인해 계산의 효율성이 저하된다. 본 연구에서는 이 문제를 해결하기 위해 모멘트 피팅법을 응용한 선택적 확장기법(Duster and Allix, 2020)을 토대로 새로운 고효율 확장 기법을 제시하였다. 특히, 적분과정에서의 비효율성에 초점을 두고 두가지 개선 방안을 제안하고 이를 수치 예제를 통해 검증하였다. 첫째로 음함수-모멘트간 효율적 계산을 위해 인공신경망을 도입하였으며, 기존 확장 기법에 비해 해의 정확성이 유지되면서도 효율적인 계산이 가능함을 확인하였다. 더불어, 구조 해석과 형상 표상용 격자를 분리, 낮은 밀도의 구조 해석 격자에서도 정확성이 향상되었음을 보였다.

키워드

모멘트 피팅법

인공신경망

적응적 구적법

레벨셋 함수

References

Babuska, I., Melenk, J.M. (1997) The Partition of Unity Method, Int. J.Numer. Methods Eng., 40(4), pp.727~758. 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N

Belytschko, T., Black, T. (1999) Elastic Crack Growth in Finite Elements with Minimal Remeshing, Int. J. Numer. Methods Eng., 45(5), pp.601~620. 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S

Düster, A., Allix, O. (2020) Selective Enrichment of Moment Fitting and Application to Cut Finite Elements and Cells, Comput. Mech., 65(2), pp.429~450. 10.1007/s00466-019-01776-2

Jamshid, P., Alexander, D., Ernst, R. (2007) Finite Cell Method, Comput. Mech., 41, pp.121~133. 10.1007/s00466-007-0173-y

Mousavi, S.E., Sukumar, N. (2011) Numerical Integration of Polynomials and Discontinuous Functions on Irregular Convex Polygons and Polyhedrons, Comput. Mech., 47(5), pp.535~554. 10.1007/s00466-010-0562-5

Strouboulis, T., Babuska, I., Copps, K. (2002) The Design and Analysis of the Generalized Finite Element Method, Comput. Methods Appl.Mech. & Eng., 181(1-3), pp.43~69. 10.1016/S0045-7825(99)00072-9

Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 35
No :5
Pages :267-275
Received Date : 2022-06-21
Revised Date : 2022-07-15
Accepted Date : 2022-07-18
DOI :https://doi.org/10.7734/COSEIK.2022.35.5.267

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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