本文給予適當的應力-應變關係、模型、網格元素、邊界條件與負載條件，則有限元素分析軟體ANSYS workbench 19.0可使用來描述有多餘圓孔的6061-T6圓孔管在循環彎曲負載下的力學行為(彎矩－曲率關係和橢圓化－曲率關係)，其中多餘圓孔的圓孔直徑大小與圓孔管的圓孔直徑大小相同，本研究共考慮五種不同的圓孔直徑分別為:2、4、6、8與10 mm，而多餘圓孔與圓孔管的圓孔方向夾角則考慮五種不同的角度分別為:45°、67.5°、90°、135°與180°。從先前的實驗結果顯示，從第一圈起彎矩－曲率關係即形成一穩定的迴圈，且圓孔直徑與圓孔方向對該曲線並沒有太大的影響。此外，隨著循環圈數的增加，橢圓化-曲率關係則呈現棘齒、不對稱、蝴蝶結狀的增加趨勢，且圓孔直徑與圓孔方向對該曲線有強烈的影響。最後，理論分析與實驗結果相互比較後可發現，有限元素ANSYS可以合理的描述實驗結果。

In this study, the finite element software ANSYS Workbench 19.0 is used to analyze the mechanical response of round-hole tubes with a redundant hole on the same cross-section and different directions under the symmetrical curvature-controlled cyclic bending. The material of the tubes is 6061-T6 aluminum alloy and the hole diameters are 2, 4, 6, 8 and 10 mm. Five different directions of the redundant holes are 45°, 67.5°, 90°, 135° and 180°. The mechanical response includes the moment-curvature and ovalization-curvature relationships. The controlled curvature is from +0.4 m-1 to -0.4 m-1. According to the experimental and analysis result, the diameter and direction of the redundant hole don’t have too much influence on moment-curvature curves. The moment-curvature curves show a stable loop. However, the ovalization-curvature curves show that the ovalizations from large to small for a fixed diameter are in the order of 45°, 67.5°, 90°, 135° and 180°. However, the ovalization-curvature curves show a strong influence by different diameter and direction of the redundant hole. 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, International Journal of Solids and Structures, Vol. 18, No. 11, pp. 957-973 (1982).
2. 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).
3. S. Kyriakides and P.K. Shaw, Inelastic Buckling of Tubes under Cyclic Bending, Journal of Pressure Vessel and Technology, Vol. 109, No. 2, pp. 169-178 (1987).
4. 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).
5. W. F. Pan, T. R. Wang and C. M. Hus, A Curvature- Ovalization Measurement Apparatus for Circular Tubes under Cyclic Bending,” Experimental Mechanics, Vol. 38, No. 2, pp. 99-102 (1998).
6. 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).
7. W. F. Pan, K. L. Lee 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).
8. 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).
9. 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，成功大學工程科學系學位論文(2006)。
10. 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).
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. 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).
13. 林均澤，有限元素分析有相同截面不同方向多餘圓孔的圓孔管承受循環彎曲負載下之行為，成功大學工程科學系碩士論文(2019)。
14. 楊善淵，相同截面不同方向的多餘圓孔對圓孔管承受循環彎曲負載下行為影響之實驗研究，成功大學工程科學系學位論文(2019)。
15. 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. 陳昱安，有多餘圓孔的圓孔管在循環彎曲負載下行為與失效之實驗研究，成功大學工程科學系學位論文(2020)。