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논문 기본 정보
- 자료유형
- 학위논문
- 저자정보
- 지도교수
- 이경훈
- 발행연도
- 2021
- 저작권
- 부산대학교 논문은 저작권에 의해 보호받습니다.
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The mechanical characteristics of unit cell models are of great interest to engineers as it appears in various materials, such as porous medium and periodic composite. To perform multiple analyses of composites in an effective way, this research proposes a parameterization technique that characterizes the fiber volume variation of unit cell models. The goal is to decrease the involvement in re-meshing for each geometrical configuration during numerical evaluations. For this purpose, the study introduces a suitable domain decomposition technique and formulate adequate mapping functions for two unit-cell models: square and hexagonal configurations. The proposed approach is twofold: (i) a nonaffine mapping function that represents the volumetric changes of fiber in a unit cell with a fiber radius, and (ii) the empirical interpolation method (EIM), which approximates the nonaffine transformation tensor as a sum of affine terms. Using the two techniques, we may quickly express different unit cell configurations as varying the fiber radius, thanks to the offline-online decomposition strategy in reduced basis (RB) approximation. For demonstration purposes, this study investigates two numerical examples: square and hexagonal unit cell models under tension and shear loads, respectively. Numerical investigation shows that the proposed techniques allow reduced basis models to result in solutions quite similar to those obtained by the corresponding finite element models at much less computational cost.
목차
Chapter 1 1Introduction 11.1 Motivation 11.2 Literature review 21.3 Thesis outline 3Chapter 2 5Geometrically parameterized partial differential equation 52.1 Review of linear elasticity 52.2 Parameterized weak form 72.3 Geometric parameterization strategies 82.4 Reference domain formulations 18Chapter 3 20Reduced basis method 203.1 Reduced space construction and error estimation 203.2 Offline/online decomposition strategy 223.3 Empirical interpolation method 23Chapter 4 26Demonstration 1: a square unit cell 264.1 Square unit cell under tension loads 264.2 Results and discussion 29Chapter 5 35Demonstration 2: a hexagonal unit cell 355.1 Hexagonal unit cell under shear load 355.2 Results and discussion 37Chapter 6 43Conclusion and Future Work . 43Bibliography 45
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