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Development of an Improved Domain Decomposition Approach using Lagrange Multipliers for Large-scale Structural Analysis
Lagrange 승수법을 이용한 영역분할 기반 대용량 구조해석 기법 개발

DC Field Value Language
dc.contributor.advisor신상준-
dc.contributor.author곽준영-
dc.date.accessioned2017-07-13T06:12:24Z-
dc.date.available2017-07-13T06:12:24Z-
dc.date.issued2014-02-
dc.identifier.other000000016846-
dc.identifier.urihttps://hdl.handle.net/10371/118353-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 기계항공공학부, 2014. 2. 신상준.-
dc.description.abstract본 논문에서는 유한요소 영역분할 구조해석 문제에 ALF 기법을 도입하여, 구조물 시스템의 제약조건에 페널티 계수를 추가하는 개선된 FETI 기반 영역분할 기법을 개발하였다. 제안된 영역분할 기법에서는 분할된 부영역 사이 공유면에 상위 격자 절점을 생성하여 전역-국부 혼합 또는 국부 Lagrange 승수를 도입하고, 시스템 변위장 방정식을 유도하는 과정에서 해의 수렴성에 영향을 주는 유연도 행렬을 재정의 하였다. 그 결과 공유면 유연도 행렬의 조건수는 이상적인 경우에 가깝게 수렴하였다. 계산 효율성의 검증을 위하여 순차 계산, 병렬 계산 프로그램을 개발하여 기존의 FETI-DP 기법과 계산 시간과 메모리 사용량을 비교하였다. 또한 본 논문에서 새롭게 제시된 예조건화 기법에 의하여 각 부영역에서의 국부 강성행렬과 공유면의 강성행렬에 직접해법을 도입할 수 있게 되었으며, 그 효율성을 수치해석을 통해 증명하였다. 제시된 FETI-local 기법의 동적 영역으로의 확장을 위하여 Newmark과의 결합이 수행되었고, 기존의 FETI 기법 및 MSC/NASTRAN과의 비교를 통하여 방법의 유효성을 증명하였다. 개발된 대용량 영역분할 구조해석 기법은 CFD 모델과의 결합을 통하여 유체-구조 연계해석 (FSI) 프로그램으로 확장되었다. 본 논문에서 개발된 영역분할 구조해석 기법은 다양한 2차원 및 3차원 대용량 구조해석 문제에 사용이 용이하며, 고정밀 유체-구조 연동 해석에 활용될 것으로 기대된다.-
dc.description.abstractAn improved computational algorithm based on a finite element domain decomposition technique is developed in this thesis. The combined use of the localized Lagrange multiplier technique and of the penalty method provides additional flexibility in the development of the algorithm. It is expected that the presently developed domain decomposition algorithm can be easily applied to structural problems, such as the two-dimensional and three-dimensional large-scale problems and expanded to the area of fluid-structure interaction analysis. In a serial implementation, the overall behavior of the proposed FETI-mixed and FETI-local are comparable to that of the FETI-DP approach in terms of computational efficiency and memory usage. In parallel implementation, the overall behavior of the proposed FETI-local compares well with that of the FETI-DP approach. The proposed approach has an advantage that it allows use of a general direct method for computation in each sub-domain. A transient time computational algorithm is developed by extending the proposed FETI-local method. The numerical computations obtained by the proposed transient time FETI-local method are presented for a two-dimensional and three dimensional problems. The transient analysis show good agreement with those obtained by FETI-DP and MSC/NASTRAN. Fluid-structure interaction analysis using the proposed transient FETI-local method and the CFD analysis is performed. The dominant frequency is 138Hz, and it agrees with experimental frequency, without center-body. The main factor that decides dominant frequency is length of the inlet.-
dc.description.tableofcontentsAbstract i
Contents iii
List of Tables vi
List of Figures vii
Chapter 1 Introduction 1
1.1 Background and Motivation 1
1.2 Finite Element Tearing and Interconnecting Method 5
1.3 Domain Decomposition Method with Direct Solver 7
1.4 Thesis Scope and Outline 8
Chapter 2 Overview of Finite Element Tearing and Interconnecting Methods 12
2.1 Algorithm of the Original FETI Method 12
2.2 Solution Strategies of the Original FETI Methods 17
2.2.1 Solution Strategy of the Original FETI Method 17
2.2.2 Solution Strategy of the Two-level FETI Method 18
2.2.3 Solution Strategy of the Dual-primal FETI Method 20
Chapter 3 Development of the Proposed Domain Decomposition Approach 24
3.1 Formulation of the Proposed Domain Decomposition Approach: FETI-mixed 25
3.2 Proposed Approach with Localized Lagrange Multiplier: FETI-local 31
3.2.1 Localized Lagrange Multiplier Technique 31
3.2.2 Strain Energy of the System 35
3.2.3 Potential of the Externally Applied Loads 36
3.2.4 Potential of a Typical Constraint 37
3.2.5 Assembly Procedure of the Constraints 40
3.2.6 Governing Equations of the Proposed FETI-local Method 43
3.2.7 Physical Interpretation of the Proposed Approach 44
3.3 Connection Strategy of the Proposed Approach 47
Chapter 4 Solution Strategy of the Proposed Approach 59
4.1 Solution Strategy of the Proposed FETI-mixed 60
4.2 Solution Strategy of the Proposed FETI-local 62
4.3 Parallel Computing Algorithm 63
Chapter 5 Application to a Structural Problem 68
5.1 Serial Implementation of the Proposed Approach 69
5.1.1 Condition Number of the Flexibility Matrix 70
5.1.2 Comparison of FETI Methods with a Fixed Number of Sub-domains 71
5.1.3 Comparison of FETI Methods with Varying Number of Sub-domains 72
5.2 Parallel Implementation of the Proposed FETI-local Approach 73
5.2.1 Two-dimensional Problem 75
5.2.2 Three-dimensional Problem 79
Chapter 6 Application to a Realistic Large-scale Problem 98
6.1 Aerodynamic Modeling 98
6.2 Structural Modeling 101
6.3 Fluid-structure Interaction Scheme 105
6.4 Transient Time FSI Analysis 105
Chapter 7 Conclusion 122
7.1 Summary 122
7.2 Future Works 126
References 128
Appendix 139
A. Serial Implementation of the Proposed FETI-mixed with Sparse Solver 139
B. Serial Implementation of the Proposed FETI-local for Various Number of the Sub-domains 140
C. Application of the Proposed FETI-local Algorithm to a Multibody Structure 141
Abstract (Korean) 150
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dc.formatapplication/pdf-
dc.format.extent3200619 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectDomain decomposition method-
dc.subjectAugmented Lagrangian Formulation-
dc.subjectFinite element tearing and interconnecting-
dc.subjectLocalized Lagrange multiplier-
dc.subjectPenalty method-
dc.subjectFluid-structure interaction-
dc.subject.ddc621-
dc.titleDevelopment of an Improved Domain Decomposition Approach using Lagrange Multipliers for Large-scale Structural Analysis-
dc.title.alternativeLagrange 승수법을 이용한 영역분할 기반 대용량 구조해석 기법 개발-
dc.typeThesis-
dc.description.degreeDoctor-
dc.citation.pagesix, 151-
dc.contributor.affiliation공과대학 기계항공공학부-
dc.date.awarded2014-02-
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Mechanical Aerospace Engineering (기계항공공학부)Theses (Ph.D. / Sc.D._기계항공공학부)
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