本研究主要是以有限元素軟體ANSYS14.0分析不同深度的尖銳凹槽SUS304不鏽鋼圓管，承受對稱曲度控制循環彎曲負載的下的力學行為，其中包含有彎矩-曲度及橢圓化-曲度的關係。循環彎曲的曲度控制在+0.1 至-0.1 m-1之間，而尖銳凹槽的深度考慮0.2、0.4、0.6、0.8和1.0 mm。
根據Lee [1]的實驗結果顯示，尖銳SUS304不鏽鋼圓管在對稱曲度控制循環彎曲下的彎矩-曲度關係，呈現隨著循環次數的增加漸趨於穩定的現象，且凹槽深度越深迴圈會越小。至於橢圓化-曲度關係則呈現棘齒、不對稱和成長的趨勢，且凹槽深度越深不對稱的情形會越明顯，橢圓化成長速度也會越快。經由ANSYS分析和實驗結果比較後發現，模擬數值雖與實驗值有些許差異，但兩者的趨勢幾乎相同。

In this study, the finite element software is used to analyze the mechanical behavior of the sharp-notched SUS 304 stainless steel tubes with different notch depths (0.2, 0.4, 0.6, 0.8 and 1.0 mm) under curvature-controlled symmetrical cyclic bending. The behavior includes the moment – curvature and ovalization – curvature relationship. The controlled curvature of the cyclic bending is from +0.1 to -0.1 m-1.
According to the experimental data from Lee [1], the relationship of moment – curvature shows gradually steady with the number of cycle for sharp-notched SUS304 stainless steel tubes under curvature-controlled symmetrical cyclic bending. The deeper the notch, the smaller is the loop. For the relationship of the ovalization – curvature, it exhibits the ratcheting, unsymmetrical and increasing phenomenon. The deeper the notch, the unsymmetrical phenomenon is more obvious and the growth speed of the ovalization is faster. Through the comparison between the ANASYS analysis and experimental data, little difference is found. But the trend is almost the same.

1.K. L. Lee, “Mechanical Behavior and Buckling Failure of Sharp-notched Circular Tubes under Cyclic Bending”, International Journal of Structural Engineering and Mechanics (SCI), Vol. 34, No. 3, pp. 367-376, 2010
2.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
3.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
4.S. Kyriakides and P. K. Shaw, “Inelastic Buckling of Tubes under Cyclic Bending,＂ASME,J. of Pressure Vessel Tech., Vol.109, pp.169-178, 1987
5.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
6.E. E. Cornoa 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
7.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
8.E. Cornoa and S. P. Vaze, “Buckling of Elastic-Plastic Square Tubes under Bending, ＂Int. J. Mech. Sci., Vol.38, No.7, pp.753-775, 1996
9.M. Elchalakani, X. L. Zhao, M. ASCE and R. Grzebieta, “Cyclic Bending Tests to Determine Fully Ductile Section Slenderness Limits for Cold-Formed Circular Hollow Sections,＂J. Struct. Eng, Vol.130, Issue 7, pp.1001-1011, 2004
10.M. Elchalakani and X. L. Zhao, “Concrete-filled cold-formed circular steel tubes subjected to variable amplitude cyclic pure bending,＂Engineering Structures, Vol.30, Issue 2, pp.287-299, 2008
11.W. F. Pan and Y. S. Her, “Viscoplastic Collapse of Thin- Walled Tubes under Cyclic Bending,＂ASME, J. of Engineering Materials and Tech., Vol.120, pp.287-290, 1998
12.W. F. Pan, T. R. Wang and C. M. Hsu, “A Curvature-Ovalization Measurement Apparatus for Circular Tubes under Cyclic Bending,＂Experimental Mechanics, Int.J., Vol.38, No.2, pp. 99-102, 1998
13.W. F. Pan and C. H. Fan, “An Experimental Stady on the Effect of Curvature-Rate at Preloading Stage on Subsequent Creep or Relaxation of Thin-Walled Tubes under Pure Bending,＂JSME Int. J., Series A, Vol.41, No.4, pp.525-531,1998
14.K. L. Lee, W. F. Pan and J. N. Kuo, “The Influence of the Diameter-to-Thickness Ratio of the Stability of Circular Tubes under Cyclic Bending,” International Journal of Solids and Structures, Vol. 38, pp. 2401-2413, 2001
15.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
16.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
17.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
18.M. M. Shokrieh and D. Rezaei, “Analysis and optimization of a composite leaf spring,” Composite Structures, Vol. 60, pp. 317-325, 2003
19.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
20.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
21.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
22.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
23.G. Li, Q. Jiang, J. Bai and J. Jiang, “Finite element analysis on dynamic behavior of gangue concrete-filled circular steel tube beam,＂Advanced Materials Research, Vol.163-167, pp.2162-2166, 2011
24.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
25.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
26.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
27.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
28.李輝煌, ”ANSYS工程分析-基礎與觀念,”高立圖書有限公司, 2005
29.Huei-Huang Lee, “Finite Element Simulations with ANSYS Worckbench 12,＂GOTOP INFORMATION INC.., Taiwan, 2010.
30.“ANSYS Structural Analysis Guide, Release 14.0,＂ANSYS, Inc., 2011.