在給予材料性質、應力-應變關係、模型、網格、邊界條件及負載條件後，本文使用有限元素軟體ANSYS Workbench 2019 R1來描述平均曲率對6061-T6圓孔管在循環彎曲負載下的力學行為(彎矩－曲率與橢圓化－曲率的關係)，至於平均曲率的影響則是考慮四種不同曲率比r (最小曲率/最大曲率)，分別為-1、-0.5、0與0.5。本研究選擇控制的最大曲率為+0.5 m-1，則r = -1時曲率控制在-0.5 m-1 ~ +0.5 m-1之間，r = -0.5時曲率控制在-0.25 m-1 ~ +0.5 m-1之間，r = 0時曲率控制在0 m-1 ~ +0.5 m-1之間，r = 0.5時曲率控制在+0.25 m-1 ~ +0.5 m-1之間，而圓孔管的圓孔直徑則分別為:2、4、6、8與10 mm。由實驗[17]與ANSYS分析的結果顯示，在固定r時，圓孔直徑大小對彎矩－曲率的關係沒有太大的影響，但圓孔直徑大小對橢圓化－曲率的關係則有強烈的影響，且圓孔直徑越大時橢圓化增加就越快。當r = -1時，循環彎矩－曲率的關係從第一圈開始即呈現出一個彈-塑性且穩定的迴圈，至於橢圓化－曲率的關係則呈現不對稱、蝴蝶結狀且增加的趨勢。當r = -0.5、0與0.5時，循環彎矩－曲率的關係從第二圈開始即呈現出一個彈性的線性重疊路徑，且隨著循環圈數的增加，彈性的線性重疊路徑會些許鬆弛後即呈現一穩定的線性重疊路徑，由於變形皆在彈性的範圍內，也因此橢圓化－曲率的關係呈現非常緩慢的增加趨勢。

In this study, the finite element software ANSYS Workbench 2019 R1 is used to analyze the effect of mean curvature on the mechanical response of round-hole tubes subjected to cyclic bending. The material of the tubes is 6061-T6 aluminum alloy and the hole diameters are 2, 4, 6, 8 and 10 mm. To highlight the influence of mean curvature effect, four different curvature ratios (minimum curvature/maximum curvature) are used in this study. The curvature ratios are -1, -0.5, 0 and +0.5. The mechanical response includes the moment-curvature and ovalization-curvature relationships. The maximum controlled curvature is +0.5 m-1. According to the experimental and analysis result, the diameter of the round hole has no influence on moment-curvature curves but has a strong influence on ovalization-curvature curves. The moment-curvature relationship is a stable loop from the first bending cycle when r = -1. However, when r = -0.5, 0 and 0.5, it presents an elastic linear overlapping path from the second bending cycle. As for the ovalization-curvature relationships, it is found that with the increase of the number of bending cycles, the curve shows an increasing, asymmetrical, ratchetting, and baw-shape trend when r = -1. However, because the deformation is within the range of elasticity, the curve presents a slowly increasing trend when r = -0.5, 0 and 0.5. In addition, it can be found that a larger diameter of the round hole leads to a faster increase of the ovalization. The ANSYS analysis was compared with the experimental finding. The simulated results exhibited close correspondence to those obtained from the experiments.

1. S. Kyriakides and P.K. Shaw, Inelastic analysis of thin-walled tubes under cyclic bending, International Journal of Solids and Structures, Vol. 21, No. 11, pp. 1073-1110 (1985).
2. S. Kyriakides and P. K. Shaw, Inelastic buckling of tubes under cyclic bending, ASME Journal of Pressure Vessel and Technology, Vol. 109, No. 2, pp. 169-178 (1987).
3. S.Kyriakides and E.Corona, An experimental investigation degradation and buckling of circular tubes under cyclic bending and external pressure, Thin-Walled Structures, Vol. 12, No. 3, pp. 229-263 (1991).
4. 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).
5. 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).
6. 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).
7. 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).
8. K. L. Lee, C. M. Hsu and W. F. Pan, The influence of mean curvature 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).
9. 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).
10. F. Salguero, S. Romero, F. Prat, Ricardo Arribas and Francisco J. Moreno, Universal Stress-Strain Equation for Metallic Materials, Journal of Materials in Civil Engineering, Vol. 26 issue 8 (2014).
11. 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).
12. C. C. Chung, K. L. Lee and W. F. Pan, Finite element analysis on the response of 6061-T6 aluminum alloy tubes with a local sharp cut under cyclic bending, Journal of Vibroengineering, Vol. 18, No. 7, pp. 4276-4284 (2016).
13. 吳尚儒，有限元素法分析圓孔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(2018)。
14. 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).
15. K. L. Lee, L. C. Chin and W. F. Pan, Elastoplastic response and failure of round-hole tubes under cyclic bending, Informatica, Vol. 31, No. 4, pp. 23-41 (2020).
16. 汪芊蓉，有多餘圓孔的圓孔管在循環彎曲負載下行為之理論分析，國立成功大學工程科學研究所碩士論文(2020)。
17. 金力中，循環彎曲負載下平均曲率對圓孔管響應與失效影響之實驗研究，國立成功大學工程科學研究所碩士論文(2021)。