本文以有限元素軟體ANSYS Workbench 15.0分析不同尖銳凹痕深度之6061-T6鋁合金圓管，承受對稱曲度控制循環彎曲負載下之力學行為。其中的學行為有:彎矩-曲度和橢圓化-曲度關係，不同的凹痕深度為:0、0.3、0.6、0.9及1.2 mm，而曲度控制在±0.4m-1之間。由分析結果顯示，不論有無凹痕，圓管在彎矩-曲度關係皆呈現穩定迴圈的形式，而橢圓化-曲度關係則呈現棘齒狀成長的趨勢。若比較不同凹痕深度的分析結果，會發現，凹痕深度對於彎矩-曲度關係並沒有太大影響，而無凹痕時橢圓化-曲度關係呈現對稱成長的趨勢，有凹痕時則呈現不對稱成長的趨勢，且凹痕深度越深，不對稱的現象越明顯，橢圓化增長也越快速。最後，本文將ANSYS分析的結果與實驗結果作比較，結果顯示，ANSYS的分析能合理的描述實驗結果。

In this study, the finite element software ANSYS Workbench 15.0 is used to analyze the mechanical response of local sharp-dented 6061-T6 aluminum alloy tubes submitted to symmetrical curvature-controlled cyclic bending. The mechanical response includes the moment-curvature and ovalization-curvature relationships, the dent depths are 0, 0.3, 0.6, 0.9 and 1.2 mm, the controlled curvature is ±0.4 m-1. According to the analysis result, the moment-curvature curves show a stable loop for tubes with or without a dent. However, the ovalization-curvature curves exhibit an increasing and ratcheting manner with the number of cycles. By comparing the analysis result for different dent depths, the moment-curvature curves reveal almost no influence by the variation of dent depths. But the ovalization-curvature curves show a symmetrical trend for tubes without a dent and unsymmetrical trend for tubes with a dent. In addition, deeper dent depths lead to more sever unsymmetrical trend and faster increase of ovalization. Finally, by comparison of the ANSYS analysis and the experimental finding, it can be found that the ANSYS analysis can properly simulate the experimental data.

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.Kyriakids, S, and Shaw, P.K,“Inelastic Buckling of Tubes under Cyclic Loads,”ASME Journal of Pressure Vessel Technology, Vol,109, pp169-178,1987.
4.E. Corona 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.
5.E. Corona and S. Kyriakides, “An Expermental 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.W. F. Pan, T. R. Wang and C. M. Hsu, A curvature-ovalizationmeasurement apparatus for circular tubes under cyclic bending, Experimental Mechanics, Vol. 38, No. 2, pp.99-102, 1998.
8.W. F. Pan and Y. S. Her, Viscoplastic collapse of thin-walled tubes under cyclic bending, Journal Engineering Materials and Technology, Vol. 120, No. 4, pp. 287-290, 1998.
9.W. F. Pan and C. H. Fan, 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.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.
11.W. F. Pan and K. L. Lee, The effect of mean curvature on the response and collapse of thin-walled tubes under cyclic bending, JSME International Journal, Series A, Vol. 45, No. 2, pp. 309-318 , 2002.
12.K. L. Lee and W. F. Pan, Pure bending creep of SUS304 stainless steel tubes, Steel and Composite Structures, Vol. 2, No. 6, pp. 461-474 , 2002.
13.徐建民、李國龍和潘文峰，圓管在對稱與不對稱循環彎曲負載下力學行為之實驗研究，技術學刊，第十八卷，第二期，257-262頁(2003)。
14.K. L. Lee, W. F. Pan and C. M. Hsu, Experimental and theoretical evaluations of the effect between diameter-to-thickness ratio and curvature-rate on the stability of circular tubes under cyclic bending, JSME International Journal, Series A, Vol. 47, No. 2, pp. 212-222 , 2004.
15.徐日豐、徐建民和潘文峰，圓管在循環彎曲負載下力學行為之理論研究，技術學刊，第二十卷，第三期，305-313頁(2005)。
16.K. H. Chang, C. M. Hsu, S. R. Sheu and W. F. Pan, Viscoplastic response and collapse of 316L stainless steel under cyclic bending,Steel and Composite Structures, Vol. 5, No. 5, pp. 359-374 , 2005.
17.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.
18.張高華、李國龍和潘文峰，圓管承受循環彎曲負載截面變形量測器之設計，技術學刊，第二十三卷，第一期，21-28頁(2008)。
19.K. H. Chang, W. F. Pan and K. L., Mean moment effect on circular thin-walled tubes under cyclic bending,Structural Engineering and Mechanics, Vol. 28, No. 5, pp. 495-514 , 2008.
20.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.
21.K. L. Lee, C. Y. Hung, H. Y. Chang and W. F. Pan, Buckling life estimation of circular tubes of different materials under cyclic bending of each cross-section of circular tube under cyclic bending,Journal of Chinese Institute Engineers, Vol. 33, No. 2, pp. 177-189 , 2010.
22.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.
23.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 Chinese Institute Engineers, Vol. 34, No. 1, pp. 75-86 , 2011.
24.K. L. Lee, C. M. Hsu and W. F. Pan, The influence of diameter-to-thickness ratios on the response and collapse of sharp-notched circular tubes under cyclic bending,Journal of Mechanics, Vol. 28, No. 3, pp. 461-468 , 2012.
25.李國龍、洪兆宇和潘文峰，循環彎曲負載下橢圓形凹槽圓管皺曲損壞之實驗分析，中正嶺學報，第四十一卷，第二期，183-190頁(2012)。
26.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.
27.K. L. Lee, C. M. Hsu and W. F. Pan, Viscoplastic collapse of sharp-notched circular tubes under cyclic bending, Acta Mechanics SolidaSinica, Vol. 26, No. 6, pp. 629- 641 , 2013.
28.K. L. Lee, C. M. Hsu and W. F. Pan, Response of sharp-notched circular tubes under bending creep and relaxation,Mechanical EngineeringJournal, Vol. 1, No. 2, pp. 1-14 , 2014.
29.K. L. Lee, Y. T. Chan and W. F. Pan, Finite element ANSYS analysis of the behavior for 6061-T6 aluminum tubes under cyclic bending with external pressure,Journal of Civil Engineering and Architecture, Vol. 8, No. 6, pp. 673-679 , 2014.
30.K. L. Lee, C. H. Mengand W. F. Pan, The influence of notch depth on the response of local sharp-notched circular tubes under cyclic bending, Journal of Applied Mathematics and Physics, Vol. 2, No. 6, pp. 335-341, 2014.
31.K. L. Lee, Y. Wang and W. F. Pan, Finite element analysis on the response of local sharp-notched circular tubes under cyclic bending, Key Engineering Materials, Vol. 626, pp. 34-39, 2015.
32.H. H. Lee, “Finite Element Simulations with ANSYS Workbench 15, ＂GOTOP INFORMATION INC., Taiwan, 2014.
33.孟慶勳, “有限元素分析局部凹痕圓管在循環彎曲負載下之行為. ＂成功大學工程科學系學位論文 (2015)。
34.李致頤, “局部尖銳凹痕圓管在循環彎曲負載下行為及毀損之研究. ＂成功大學工程科學系學位論文 (2016)。