本研究針對具不均勻微觀構件之蜂巢材料力學性質進行廣泛性之研究，首先建立一具不均勻斷面之理論模型，並利用巨觀參數相對密度 與微觀參數 定義其剖面形貌，並以樑之變形理論進行理論分析，包括楊氏模數、剪力模數、柏松比、彈性挫曲強度、塑性崩塌強度與雙軸載重之降伏包絡線，結果發現力學性質與其相對密度與微觀參數息息相關，且各力學性質隨著微觀參數變化之趨勢皆為類似，並表示存在最佳微觀結構之可能。因此，利用其數值結果建立各力學性質與相對密度之關係式，其關係式除了可以準確估計其力學性質之外，並提供最佳化微觀構件之設計圖表，以利工程實際運用所需。此研究之概念與方法將可運用於研究具不均勻微觀構件之泡沫材料力學性質。

An elastic model for honeycombs with Plateau borders is utilized to investigate its mechanical properties and the effects of solid distribution. The profile of cell edge can be defined by relative density and the volume fraction of solid contained in Plateau borders region, hence, the mechanical properties such as Young’s modulus, shear modulus, Poisson’s ratio, elastic buckling, plastic collapse strength and yield surface can be analytical examined by assuming the cell edge as a beam member. As the results, the mechanical properties of honeycombs with Plateau borders depend on both relative density and the volume fraction of solid contained in Plateau borders region. In addition, the effects of solid distribution on these mechanical properties have a similar trend which is an optimal microstructure might exist for honeycombs with Plateau borders. In order to predict these mechanical properties, the relationships between mechanical properties and relative density are proposed based on the numerical results. Furthermore, the design maps of stiffness and strength for regular honeycombs are provided to optimize the microstructure of honeycombs for engineering demand. The methods utilized in the present work still can be applied to analyze the mechanical properties of open-cell foam with non-uniform cell edges.

Table of Contents

Acknowledgements……………………………………………………III
Table of Contents…………………………………………………………IV
Figures List………………………………………………………………………VI
Tables List………………………………………………………………………XI
Chinese Abstract……………………………………………………………………XIII
English Abstract……………………………………………………………………XIV
Chapter 1 Introduction………………………………………………………………1
1.1 Literature Review……………………………………………………1
1.2 Cell Geometry………………………………………………………5
Chapter 2 Elastic Moduli and Plastic Collapse Strength……………………………17
2.1 Deflection of a Variable-Thickness Cell Edge……………………18
2.2 Elastic Moduli………………………………………………………20
2.3 Plastic Collapse Strength……………………………………………25
2.4 Results and Discussion………………………………………………28
2.5 Summary……………………………………………………………32
Chapter 3 Elastic Buckling Strength…………………………………………………45
3.1 Rotational Stiffness…………………………………………………46
3.2 Critical Buckling Load……………………………………………49
3.3 Numerical Examples and Discussions………………………………56
3.4 Summary……………………………………………………………60
Chapter 4 Yield Surface……………………………………………………………68
4.1 Yield Caused by Axial Force and Bending Moment…………………69
4.2 Yield Caused by Axial Force at The Mid-span of Each
Inclined Cell Edge…………………………………………………73
4.3 Yield Caused by Shear Force at The Mid-span of
Each Inclined Cell Edge……………………………………………76
4.4 Discussion…………………………………………………………78
4.5 Summary……………………………………………………………81
Chapter 5 Relationship between Mechanical Properties and Relative Density……92
5.1 Exponent Constant…………………………………………………94
5.2 Microstructural Coefficient…………………………………………96
5.3 Modified Theoretical Expressions…………………………………97
5.4 Optimal Value of ………………………………………………98
5.5 Design Maps for Stiffness and Strength……………………………99
5.6 Summary……………………………………………………………100
Chapter 6 Conclusions and Suggestions……………………………………118
6.1 Conclusions…………………………………………………………118
6.2 Suggestions…………………………………………………………121
Reference ………………………………………………………………………122
Appendix A ……………………………………………………………………125
Appendix B ……………………………………………………………………126

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