Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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A Boundary-layer Stress Analysis of Laminated Composite Beams via a Computational Asymptotic Method and Papkovich-Fadle Eigenvector

전산점근해석기법과 고유벡터를 이용한 복합재료 보의 경계층 응력 해석

  • Sin-Ho Kim (Department of Mechanical Engineering, Department of Aeronautics, Kumoh National Institute of Technology) ;
  • Jun-Sik Kim (Department of Mechanical System Engineering, Department of Aeronautics, Kumoh National Institute of Technology)
  • 김신호 (금오공과대학교 기계공학과 항공기계전자융합전공) ;
  • 김준식 (금오공과대학교 기계시스템공학과 항공기계전자융합전공)
  • Received : 2023.11.14
  • Accepted : 2023.11.29
  • Published : 2024.02.29
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Abstract

This paper utilizes computational asymptotic analysis to compute the boundary layer solution for composite beams and validates the findings through a comparison with ANSYS results. The boundary layer solution, presented as a sum of the interior solution and pure boundary layer effects, necessitates a mathematically rigorous formalization for both interior and boundary layer aspects. Computational asymptotic analysis emerges as a robust technique for addressing such problems. However, the challenge lies in connecting the boundary layer and interior solutions. In this study, we systematically separate the principles of virtual work and the principles of Saint-Venant to tackle internal and boundary layer issues. The boundary layer solution is articulated by calculating the Papkovich-Fadle eigenfunctions, representing them as linear combinations of real and imaginary vectors. To address warping functions in the interior solutions, we employed a least squares method. The computed solutions exhibit excellent agreement with 2D finite element analysis results, both quantitatively and qualitatively. This validates the effectiveness and accuracy of the proposed approach in capturing the behavior of composite beams.

본 논문에서는 전산점근해석기법을 사용하여 복합재료 보에 대한 경계층 해를 계산하고, ANSYS 결과와 비교 검증하였다. 경계층 해는 내부해와 순수 경계층 효과의 합으로 표현되기 때문에, 내부 및 경계층에 대한 수학적으로 엄밀한 정식화를 요구한다. 전산점근 해석기법은 수학적으로 매우 강력한 기법으로, 이러한 문제에 유용하다. 그러나 경계층과 내부 해들의 연결을 시키기 쉽지 않은데, 본 연구에서는 가상일의 원리를 통해 생브낭의 원리와 내부 및 경계층 문제를 체계적으로 분리하였다. 경계층 해는 팝코비치-패들 고유벡터를 계산하여, 실수부와 허수부 벡터들의 선형 조합으로 표현하고, 내부 해의 워핑 함수들을 보상할 수 있도록 최소오차 자승법을 적용하였다. 계산된 해들은 2차원 유한요소 해석 결과와 비교하여 정성적일 뿐만 아니라 정량적으로도 잘 일치하는 결과를 얻었다.

Keywords

Acknowledgement

이 연구는 금오공과대학교 학술연구비로 지원되었음(202103770001).

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