Approximately Coupled Method of Finite Element Method and 
Boundary Element Method for Two-Dimensional Elasto-static Problem

Myung-Kwan Song

doi:10.12814/jkgss.2021.20.3.011

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2021 Vol.20, Issue 3 Preview Page

Research Article

Approximately Coupled Method of Finite Element Method and Boundary Element Method for Two-Dimensional Elasto-static Problem 이차원 탄성 정적 문제를 위한 유한요소법과 경계요소법의 근사 결합 방법

30 September 2021. pp. 11-20

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Abstract

In this paper, the approximately coupled method of finite element method and boundary element method to obtain efficient and accurate analysis results is proposed for a two-dimensional elasto-static problem with a geometrically abruptly changing part. As the finite element of a two-dimensional problem, three-node and four-node plane stress element is applied, and as the boundary element of a two-dimensional problem, three-node boundary element is applied. In the modeling stage, firstly, an entire analysis target object is modeled as finite elements, and then a geometrically abruptly changing part is modeled as boundary elements. The boundary element is defined using the nodes defined for modeling finite elements. In the analysis stage, finite element analysis is firstly performed on a entire analysis target object, and boundary element analysis is automatically performed afterwards. As for the boundary conditions at boundary element analysis, displacement conditions and stress conditions, which are the results of finite element analysis, are applied. As a numerical example, the analysis results for a two-dimensional elasto-static problem, a plate with a crack, are presented and investigated.

Keywords

Two-dimensional elasto-static

Finite element

Boundary element

Coupled method

본 논문에서는 유한요소법과 경계요소법을 결합하여 기하학적으로 급변 부위가 있는 이차원 탄성 정적 문제에 대하여 효율적이고 정확한 해석 결과를 얻기 위한 유한요소법과 경계요소법의 근사 결합 방법을 제시한다. 이차원 문제의 유한요소로서는 3절점, 4절점 평면응력 요소를 적용하고, 이차원 문제의 경계요소로는 3절점 경계요소를 적용한다. 모델링 단계에서는 우선 전체 해석 대상을 유한요소로 모델링한 후에 기학학적 급변 부위를 경계요소로 모델링 하는데, 유한요소의 모델링을 위하여 정의된 절점을 이용하여 경계요소를 정의한다. 해석 단계에서는 전체 해석 대상에 대하여 유한요소 해석을 우선적으로 수행하고, 이후에 경계요소 해석을 자동으로 수행하는데, 경계부에서의 경계조건은 유한요소 해석 결과인 변위 조건과 응력 조건을 적용한다. 수치예제로서 이차원 탄성 정적 문제인 균열이 있는 평판에 대한 해석 결과를 제시하고 고찰한다.

References

Aour, B., Rahmani, O., and Nait-Abdelaziz M. (2007), A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics, International Journal of Solids and Structures, Vol.44, pp.2523-2539. 10.1016/j.ijsolstr.2006.08.001

Becker, A. A. (1992), The Boundary Element Method in Engineering, McGraw-Hill, UK.

Beer, G. (1983), Finite Element, Boundary Element, and Coupled Analysis of Unbounded Problems in Elastostatics, International Journal for Numerical Methods in Engineering, Vol.19, pp.567-580. 10.1002/nme.1620190408

Belytschko, T., Chang, H. S., and Lu, Y. Y. (1989), A Variationally Coupled Finite Element-Boundary Element Method, Computers & Structures Vol.33, No.1, pp.17-20. 10.1016/0045-7949(89)90124-7

Boumaiza, D. and Aour, B. (2014), On the efficiency of the iterative coupling FEM-BEM for solving the elasto-plastic problems, Engineering Structures, Vol.72, pp12-25. 10.1016/j.engstruct.2014.03.036

Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C. (1984), Boundary Element Techniques, Springer-Verlag, UK. 10.1007/978-3-642-48860-3

Chidgzey, S. R., Trevelyan J., and Deeks, A. J. (2008), Coupling of the Boundary Element Method and the Scaled Boundary Element Method for Computations in Fracture Mechanics, Computers & Structures Vol.86, pp.1198-1203. 10.1016/j.compstruc.2007.11.007

Cook, R.D., Malkus, D.S., Plesha, M.E. (1989), Concepts and Applications of Finite Element Analysis, John Wiley & Sons, USA.

El-Gebeily, M., Elleithy, W. M., and Al-Gahtani, H. J. (2002), Convergence of the Domain Decomposition Finite Element- Boundary Element Coupling Methods, Computer Methods in Applied Mechanics and Engineering, Vol.191, pp.4851-4867. 10.1016/S0045-7825(02)00405-X

Galvin, P., Francois, S., Schevenels, M., Bongini, E., Degrande, G., and Lombaert, G. (2010), A 2.5D Coupled FE-BE Model for the Prediction of Railway Induced Vibrations, Soil Dynamics and Earthquake Engineering, Vol.30, pp. 1500-1512. 10.1016/j.soildyn.2010.07.001

Hinton, E., Owen, D. R. J. (1977), Finite Element Programming, Academic Press Inc. Ltd.

Kim, K. H., Bang, J. S., Kim, J. H., Kim, Y., Kim, S. J., and Kim, Y. (2013), Fully Coupled BEN-FEM Analysis for Ship Hydroelasticity in Waves, Marine Structures, Vol.33, pp.71-99. 10.1016/j.marstruc.2013.04.004

Stephan, E. P. (2017), Coupling of Boundary Element Methods and Finite Element Methods, Encyclopedia Computational Mechanics, 2nd. Ed., pp.1-40. 10.1002/9781119176817.ecm200829073844

Vasilev, G., Parvanova, S., Dineva, P., and Wuttke, F. (2015), Soil-structure Interaction using BEM-FEM Coupling through ANSYS Software Package, Soil Dynamics and Earthquake Engineering, Vol.70, pp.104-117. 10.1016/j.soildyn.2014.12.007

Yazdchi, M., Khalili, N., and Valliappan, S. (1999), Dynamic Soil-Structure Interaction Analysis via Coupled Finite-Element- Boundary-Element Method, Soil Dynamics and Earthquake Engineering, Vol.18, pp.499-517. 10.1016/S0267-7261(99)00019-6

Zhao, W., Chen, L., Chen, H., and Marburg, S. (2019), Topology Optimization of Exterior Acoustic-structure Interaction Systems using the Coupled FEM-BEM Method, International Journal for Numerical Methods in Engineering, Vol.119, No.5, pp.404-431. 10.1002/nme.6055

Information

Publisher :Korean Geosythetics Society
Publisher(Ko) :한국지반신소재학회
Journal Title :Journal of the Korean Geosynthetics Society
Journal Title(Ko) :한국지반신소재학회 논문집
Volume : 20
No :3
Pages :11-20
Received Date : 2021-08-06
Revised Date : 2021-09-25
Accepted Date : 2021-09-28
DOI :https://doi.org/10.12814/jkgss.2021.20.3.011

Journal of the Korean Geosynthetics Society ISSN:2508-2876(Print) 2287-9528(Online) 한국지반신소재학회 논문집

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