本研究是以有限元素分析軟體ANSYS Workbench 14.0分析6061-T6鋁合金管具有局部切痕時，承受對稱曲度控制循環彎曲負載下之力學行為。而力學行為包含有:彎矩-曲度和橢圓化-曲度的關係。其中所考慮的切痕的深度為: 0.4、0.8、1.2、1.6和2.0 mm，切痕的方向有: 0、30、60及90度，而循環彎曲的曲度控制在+0.4 m-1至-0.4 m-1之間。
根據ANSYS結果顯示，切痕的深度對彎矩-曲度關係影響不大。但橢圓化-曲度關係則呈現棘齒狀，並隨著循環圈數成長的趨勢，且在較淺切痕深度下，曲線呈現左右對稱的關係；而在較深的切痕深度時，則曲線呈現左右不對稱的情形，且隨著切痕深度的增加，橢圓化成長的速度將會越快。此外，當考慮固定切痕的深度時，切痕的方向對彎矩-曲度關係影響不大，但橢圓化-曲度關係則隨著角度增加不對稱的現象會趨於對稱。最後，本研究的ANSYS分析也與實驗結果進行比較，結果顯示模擬數值雖與實驗值有些許差異，但兩者的趨勢卻非常相似。

In this study, the finite element software ANSYS Workbench 14.0 is used to analyze the mechanical behavior of local-chopped 6061-T6 aluminum tubes under curvature- controlled symmetrical cyclic bending. The behavior includes the relationships of the moment-curvature and ovalization-curvature. The different chopped depths include: 0.4, 0.8, 1.2, 1.6 and 2.0 mm and different chopped directions consider: 0, 30, 60 and 90. The controlled curvature of the cyclic bending is between +0.4 to -0.4 m-1.
According to the ANSYS analysis result, the chopped depth has less influence on the moment-curvature realtionship. As for the relationship of the ovalization-curvature, it exhibits the ratcheting and increasing phenomenon with the number of cycles. The relationship shows symmetrical for a shallow chop, however, the relationship shows unsymmetrical for a deeper chop. And, higher chopped depth leads to higher ovalization. In addition, when the fix chopped depth is considered, the chopped direction doesn’t have much influence on the relation between moment and curvature. But, the ovalization-curvature relationship exhibits the unsymmetrical manner with a lower chopped direction and symmetrical manner with a higher chopped direction. Finally, the ANSYS analysis is compared with the experimental data. Although some differences between the experimental and simulated results, but the trends are very similar between the experimental and simulated results.

1. S. Kyriakides and P. K. Shaw, “Response and Stability of Elastoplastic Circular Pipe under Combined Bending and External Pressure,＂Int. J. Solids Struct., Vol.18, No.11, pp.957-973, (1982)

2. P. K. Shaw and S. Kyriakides, “Inelastic Analysis of Thin-Walled Tubes under Cyclic Bending,＂Int. J. Solids Struct., Vol.21, No.11, pp.1073-1100, (1985)

3. E. Cornoa and S. Kyriakides, “On the Collapse of Inelastic Tubes under Combined Bending and Pressure,＂Int. J. Solids Struct., Vol.24,No.5, pp.505-535, (1988)

4. Corona, E., and Kyriakides, S., “On the Collapse of Inelastic Tubes under Combined Bending and Pressure,” International Journal of Solids and Structures, Vol. 24, pp. 505-535, (1988).

5. Corona, E., and Kyriakides, S., “An Experimental Investigation of the Degradation and Buckling of Circular Tubes under Cyclic Bending and External Pressure,” Thin-Walled Structures, Vol. 12, pp. 229-263, (1991).
 
6. S. Kyriakides and G. T. Ju, “Bifurcation And Localization Instabilities In Cylindrical Shells Under Bending-I. Experiment,＂Int. J. Solids Struct, Vol.29, No.9, pp.1117-1142, (1992)

7. Pan, W. F., and Leu, K. T., “Endochronic analysis for viscoplastic collapse of a thin-walled tube under combined bending and external pressure,” JSME Int. J. Ser. A 40 (2), 189-199, (1997).

8. Pan, W. F., Wang, T. R., and Hsu, C. M., “A Curvature-Ovalization Measurement Apparatus for Circular Tubes under Cyclic Bending,” Experimental Mechanics, Vol. 38, No. 2, pp. 99-102, (1998).

9. Pan, W. F., and Fan, C. H., “An Experimental Study on the Effect of Curvature-Rate at Preloading Stage on Subsequent Creep or Relaxation of Thin-Walled Tubes under Pure Bending,” JSME International Journal, Series A, Vol. 41, No. 4, pp. 525-531, (1998).

10. Lee, K. L., Pan, W. F., and Kuo, J. N., “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, pp. 2401-2413, (2001).

11. Lee, K. L., Shie, R. F., and Chang, K. H., “Experimental and Theoretical Investigation of the Response and Collapse of 316L Stainless Steel Tubes Subjected to Cyclic Bending,” JSME International Journal, Series A , Vol. 48, No. 3, pp. 155-162, (2005).

12. K. H. Chang and W. F. Pan, “Buckling life estimation of circular tubes under cyclic bending,＂International Journal of Solids and Structures, Vol.46, Issue 2, pp.254-270, (2009)

13. K. L. Lee, C. Y. Hung and W. F. Pan, “CCD digital camera system for measuring curvature and ovalization of each cross-section of circular tube under cyclic bending,＂Journal of the Chinese Institute of Engineers, Vol.34, Issue 1, pp.75-86, (2011)

14. M. M. Shokrieh and D. Rezaei, “Analysis and optimization of a composite leaf spring,” Composite Structures, Vol. 60, pp. 317-325, (2003)

15. R. Mahdavinejad, “Finite element analysis of machine and workpiece instability in turning,” International Journal of Machine Tools and Manufacture, Vol. 45, pp.753-760, (2005)

16. Z. F. Wen, X. S. Jin and W. H. Zhang, “Contact-impact stress analysis of rail joint region using the dynamic finite element method,” Wear, Vol. 258, pp.1301-1309, (2005)

17. M. X. Zhou, Q. A. Huang and Ming Qin, “Modeling, design and fabrication of a triple-layered capacitive pressure sensor,” Sensors and Actuators A：Physical, Vol.117, pp.71-81, (2005)

18. L. Fu, G. Q. Tao, Y. N. Huang and Z. Wu, “Finite Element Analysis and Experimental Investigation of Carbon Fiber Composite Circular Tube,＂Advanced Materials Research, Vol.194-196, pp.1776-1780, 2011

19. G. Li, Q. Jiang, J .Bai and J . Jiang , “Finite element analysis on dynamic behavior of gangue concretr-filled circular steel tube beam＂ Advanced Materials Research, Vol.163-167 , pp.2162-2166, 2011

20. 林俊宏, ”有限元素ANSYS分析圓管在循環彎曲負載下之力學行為,” 國立成功大學工程科學研究所碩士論文, 2006

21. 解智翔, ”有限元素ANSYS分析尖銳凹槽薄壁管在循環彎曲負載下之力學行為,” 國立成功大學工程科學研究所碩士論文, 2008

22. 林煒凱, ”有限元素ANSYS分析橢圓形凹槽薄壁管在循環彎曲負載下之力學行為,” 國立成功大學工程科學研究所碩士論文, 2008

23. 趙國鈞, ”有限元素ANSYS分析圓管在有外壓或無外壓循環彎曲負載下之力學行為,” 國立成功大學工程科學研究所碩士論文, 2009

24. 葉弘文”有限元素分析尖銳凹槽SUS304不鏽鋼圓管在循環彎曲負載下之力學行為,” 國立成功大學工程科學研究所碩士論文, 2012

25. 孫智勇”有限元素分析尖銳凹槽6061-T6鋁合金管在循環彎曲負載下之力學行為,” 國立成功大學工程科學研究所碩士論文, 2013

26. 洪揚銘” 有限元素分析局部尖銳凹槽圓管在循環彎曲負載下之行為,” 國立成功大學工程科學研究所碩士論文, 2013

27. 沈睿騰” 不同深度切痕圓管在循環彎曲負載下行為之實驗研究,” 國立成功大學工程科學研究所碩士論文, 2014

28. 吳定軒” 不同方向切痕圓管在循環彎曲負載下行為之實驗研究,” 國立成功大學工程科學研究所碩士論文, 2014

29. 李輝煌, ”ANSYS工程分析-基礎與觀念,”高立圖書有限公司,2005

30. Huei-Huang Lee, “Finite Element Simulations with ANSYS Worckbench 12,＂GOTOP INFORMATION INC.., Taiwan, 2010.