本論文主要研究不同外長軸/外短軸長度比的SUS 304不鏽鋼橢圓管在不同彎曲方向循環彎曲負載的行為，相關的行為有:外短軸變化-循環圈數與臨界外短軸變化-控制曲率的關係，其中外短軸變化定義為外短軸長度變化量/初始外短軸長度。本研究不同的外長軸/外短軸長度比分別有：1.5、2.0、2.5與3.0，而不同彎曲方向分別有：0º、30º、60º和90º，至於控制循環曲率分別有：0.5、0.6、0.7與0.8 m-1。
根據實驗結果顯示，外短軸變化-循環圈數的關係可分為四階段：初始、第二、第三與第四階段，其中到第三階段時，外短軸變化會極速的上升，並馬上進入第四階段，而在第四階段則會有一小段平緩的成長，直到SUS 304不鏽鋼橢圓管發生斷裂。由於前兩階段佔據大多數的循環圈數，所以本研究聚焦討論初始及第二階段的外短軸變化-循環圈數關係。此外，上述關係中也發現，若同時固定彎曲方向與控制曲率，外長軸/外短軸長度比越大時，外短軸變化成長就越快；若同時固定控制曲率與外長軸/外短軸長度比時，彎曲方向越大時，外短軸變化成長就越慢。至於臨界外短軸變化-控制曲率的關係中發現，當外長軸/外短軸長度比越大時，臨界外短軸變化就越大；當彎曲方向越大時，臨界外短軸變化就越大。最後，本文提出可描述外短軸變化-循環圈數與臨界外短軸變化-控制曲率關係的理論公式，並且將理論分析與實驗結果對比後發現，理論分析可合理的描述實驗結果。

This paper primarily investigates the behavior of SUS 304 stainless steel elliptical tubes with different outer major axis/outer minor axis length ratios under cyclic bending loads in different bending directions. The behaviors studied include the relationship between the outer minor axis variation and the number of cycles, as well as the relationship between the critical outer minor axis variation and the control curvature. The outer minor axis variation is defined as the variation in the length of the outer minor axis divided by the initial outer minor axis length. The different outer major axis/outer minor axis length ratios studied are: 1.5, 2.0, 2.5, and 3.0, and the different bending directions are: 0º, 30º, 60º, and 90º. The control curvatures are: ±0.5, ±0.6, ±0.7, and ±0.8 m⁻¹. According to the experimental results, the relationship between the outer minor axis variation and the number of cycles can be divided into four stages: the initial, second, third, and fourth stages. In the third stage, the outer minor axis variation increases rapidly and quickly enters the fourth stage, where there is a brief period of gradual growth until the SUS 304 stainless steel elliptical tube fractures. Since the first two stages occupy the majority of the cycles, this study focuses on discussing the relationship between the outer minor axis variation and the number of cycles in the initial and second stages. Furthermore, it was found that when the bending direction and control curvature are fixed, the larger the outer major axis/outer minor axis length ratio, the faster the outer minor axis variation grows. Additionally, when the control curvature and the outer major axis/outer minor axis length ratio are fixed, the larger the bending direction, the slower the outer minor axis variation grows. Regarding the relationship between the critical outer minor axis variation and the control curvature, it was found that the larger the outer major axis/outer minor axis length ratio, the larger the critical outer minor axis variation; and the larger the bending direction, the larger the critical outer minor axis variation. Finally, this study proposes theoretical formulas that can describe the relationship between the outer minor axis variation and the number of cycles, as well as the relationship between the critical outer minor axis variation and the control curvature. Comparing the theoretical analysis with the experimental results shows that the theoretical analysis can reasonably describe the experimental results.

1. Kyriakides S. and Shaw P. K. , “ Response and Stability of Elastoplastic Circular Pipes Under Combined Bending and External Pressure” ,International Journal of Solids and Structures , Vol. 18 , pp. 957-973 (1982) .
2. P. K. Shaw and S. Kyriakides, “Inelastic analysis of thin-walled tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 21, No. 11, pp. 1073-1100 (1985).
3. S. Kyriakides and P. K. Shaw, “Inelastic buckling of tubes under cyclic loads”, Journal of Pressure Vessel Technology, Vol. 109, No. 2, pp. 169-178 (1987).
4. E. Corona and S. Kyriakides, “On the collapse of inelastic tubes under combined bending and pressure”, International Journal of Solids and Structures, Vol. 24, No. 5, pp. 505-535 (1988).
5. E. Corona and S. Kyriakides, “An experimental investigation of the degradation and buckling of circular tubes under cyclic bending and external pressure”, Thin-Walled Structures, Vol. 12, No. 3, pp. 229-263 (1991).
6. S. Kyriakides and G. T. Ju, “Bifurcation and localization instabilities in cylindrical shells under bending – I. Experiments”, International Journal of Solids and Structures, Vol. 29, No. 9, pp. 1117-1142 (1992).
7. E. Corona and S. Vaze, “Buckling of elastic-plastic square tubes under bending”, International Journal of Mechanical Science, Vol. 38, No. 7, pp. 753-775 (1996).
8. W. F. Pan, T. R. Wang and C. M. Hsu, “A curvature-ovalization measurement apparatus for circular tubes under cyclic bending”, Experimental Mechanics, Vol. 38, No. 2, pp. 99-102 (1998).
9. K. L. Lee, W. F. Pan and J. N. Kuo, “The influence of the diameter-to-thickness ratio on the stability of circular tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 38, No. 14, pp. 2401-2413 (2001).
10. K. L. Lee, C. M. Hsu, W. F. Pan, “Endochronic Simulation for the response of 1020 carbon steel tubes under symmetric and unsymmetric cyclic bending with or without external pressure”, Steel and Composite Structures, Vol. 8, No. 2, pp. 99-114 (2008).
11. K. H. Chang and W. F. Pan, “Buckling life estimation of circular tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 46, No. 2, pp. 254-270 (2009).
12. K. L. Lee, C. Y. Hung and W. F. Pan, Variation of ovalization for sharp-notched circular tubes under cyclic bending, Journal of Mechanics, Vol. 26, No. 3, pp. 403- 411 (2010).
13. K. L. Lee, C. M. Hsu and W. F. Pan, The influence of mean curvatures on the collapse of sharp-notched circular tubes under cyclic bending, Journal of Chinese Society of Mechanical Engineering, Vol. 34, NO. 5, pp. 461-468 (2013).
14. K. L. Lee, C. C. Chung and W. F. Pan, “Growing and critical ovalization for sharp-notched 6061-T6 aluminum alloy tubes under cyclic bending”, Journal of Chinese Institute of Engineers, Vol. 39, No. 8, pp. 926-935 (2016).
15. K. L. Lee, K. H. Chang and W. F. Pan, “Effect of notch depth and direction on stability of local sharp-notched circular tubes subjected to cyclic bending”, International Journal of Structural Stability and Dynamics, Vol. 18, No. 7, 1850090 [23 pages] (2018).
16. K. L. Lee, M. L. Weng and W. F. Pan, “On the failure of round-hole tubes under cyclic bending”, Journal of Chinese Society of Mechanical Engineering, Vol. 40, No. 6, pp. 663-673 (2019).
17. K. L. Lee, Q. Y. Wen and W. F. Pan, “Response of round-hole tubes with different hole sizes and positions under pure bending relaxation”, Informatica Journal, Vol. 32, No. 8, pp. 48-65 (2021).
18. K. L. Lee, C. M. Hsu and W. F. Pan, “Response of sharp-notched circular tubes under bending creep and relaxation”, Mechanical Engineering Journal, Vol. 1, No. 2, pp. 1-14 (2014).
19. 溫慶源, “不同外徑/壁厚比與不同圓孔直徑圓孔管在循環彎曲負載下橢圓化成長與臨界橢圓化之研究”,國立成功大學工程科學研究所碩士論文(2022).
20. 張哲嘉, “不同旋轉角度與不同外長軸/外短軸長度比之SUS 304不鏽鋼橢圓管在循環彎曲負載下響應的實驗研究”,國立成功大學工程科學研究所碩士論文(2023).