Journal of the Korean Society of Marine Environment & Safety (해양환경안전학회지)

The Korean Society of Marine Environment and safety (해양환경안전학회)
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Local Nonlinear Static Analysis via Static Condensation

강성응축기법을 이용한 국부 비선형 정적 해석

  • Shin, Han-Seop (Naval Architecture and Ocean Systems Engineering, Korea Maritime & Ocean University) ;
  • Oh, Min-Han (Load and Response Research Department, Hyundai Heavy Industries) ;
  • Boo, Seung-Hwan (Naval Architecture and Ocean Systems Engineering, Korea Maritime & Ocean University)
  • 신한섭 (한국해양대학교 대학원) ;
  • 오민한 (현대중공업 운항구조연구실) ;
  • 부승환 (한국해양대학교 조선.해양시스템공학과)
  • Received : 2021.02.01
  • Accepted : 2021.02.25
  • Published : 2021.02.28
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Abstract

In this study, an analysis technique using static condensation is proposed for an efficient local nonlinear static analysis. The static condensation method is a model reduction method based on the degrees of freedom, and the analysis model is divided into a target part and a condensed part to be omitted. In this study, the nonlinear and linear parts were designated to the target and the omitted parts, respectively, and both the stiffness matrix and load vector corresponding to the linear part were condensed into the nonlinear part. After model condensation, the reduced model comprising the stiffness matrix and the load vector for the nonlinear part is constructed, and only this reduced model was updated through the Newton-Raphson iteration for an efficient nonlinear analysis. Finally, the efficiency and reliability of the proposed analysis technique were presented by applying it to various numerical examples.

본 연구에서는 국부 비선형 정적 해석을 효율적으로 수행하기 위하여 강성응축(Static condensation)을 활용한 해석기법을 제시하였다. 강성응축기법은 자유도 기반의 유한요소 모델 축소기법이며, 해석 모델을 관심 대상(Target) 부분과 응축되어 생략될(Omitted) 부분으로 구분한다. 본 연구에서는, 관심 대상 부분에는 비선형 영역, 생략될 부분에는 선형 영역으로 지정하였고, 선형 영역에 대응되는 강성 행렬 및 하중 벡터를 비선형 영역, 즉 관심 대상 부분으로 모두 응축하였다. 모델 응축 후에는 비선형 영역에 대한 강성 행렬 및 하중 벡터만으로 이루어진 축소 모델을 구성하였으며, 이 축소 모델만을 뉴턴-랩슨 반복(Newton-Raphson iteration)을 통해 갱신하여 효율적으로 비선형 해석을 수행하였다. 끝으로, 제안된 기법을 다양한 수치 예제에 적용하여 해석기법의 효율성과 신뢰성을 제시하였다.

Keywords

Acknowledgement

이 논문은 2020년 대한민국 교육부와 한국연구재단의 지원을 받아 수행된 연구임(NRF-2019R1C1C1004159). 또한, 이 논문은 2020년도 산업통상자원부의 '창의산업융합 특성화 인재양성사업'의 지원을 받아 연구되었음(과제번호 N0000717).

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