本文主要利用MARC有限元素軟體分析通過曲線模之軸對稱擠製加工問題，其結果除了以實驗[10]做驗證外，並和上界限解[12]互做比較。本文結果顯示以有限元素方法對材料變形行為及擠製壓力的預測均較上界限解為佳。
本文亦就縮減率、潤滑條件及模具曲線等加工參數對變形場及擠製壓力的有限元素解及上界限解的效應。針對這個主題，本文的結果顯示理論計值在定性上均能反應如實驗所觀察到的加工參數效應，然在定量上的比較，有限元素解亦比上界限解對該效應具有較佳的預測效果。

1.Chang K.T., and Choi J.C., "Upper-Bound Solution to Extrusion Problems Through Curved Dies," Proceedings of the 12th Midwestern Mechanics Conference, 1971, pp.383-396. University of Notre Dame, U.S.A.
2.Nagpal V., "General Kinematically Admissible Velocity Fields for Some Axisymmetric Metal Forming Problems," Journal of Engineering For Industry, Trans. ASME, Series B, Nov., 1974, pp.1197-1201.
3.Yang D.Y., Han C.H., and Lee B.C., "The Use of Generalised Deformation Boundaries for the Analysis of Axisymmetric Extrusion Through Curved Dies," International Journal of Mechanical Science, Vol.27, No.10, 1985, pp.653-663.
4.Reddy N. Venkata, Dixit P. M. and Lal G. K., "Die Design for Axiaymmetric Extrusion," Journal of Materials Processing Technology, Vol.55, December, 1995, pp. 331-339.
5.Wu C.W., and Hsu R.Q., "A universal velocity field for the extrusion of non-axisymmetric rods with non-uniform velocity distribution in the extrusion direction, " Journal of Material Processing Technology, Vol.97, 2000, pp. 180-185.
6.Alto A., Galantucci L.M. and Tricarico L., "A Parametric FEM Analysis of Extrusion Using A Personal Computer," Journal of Materials Processing Technology, Vol. 31 1992 pp.335-345.
7.Kang Beom-Soo, Kim Byung-Min, and Choi Jae-Chan, "Perform Design in Extrusion by the FEM and Its Experimental Confirmation," Journal of Materials Processing Technology, Vol.41, 1994, pp.237-248.
8.Chanda, T., and Zhou, J., and Kowalski, L., and Duszczyk, J., ŗD FEM Simulation Of The Thermal Events During AA6061 Aluminum Extrusion," Scripta Materialia, Vol. 41, No. 2, pp. 195-202, 1999.
9.Gouveia B.P.P.A., Rodrigues J.M.C., Bay N., and Martins P.A.F., "Finite-element modeling of cold forward extrusion," Journal of Materials Processing Technology Vol.94 No.2, 2000, pp.85-93
10.陳樹人, "曲線模圓桿擠製之實驗研究." 國立中央大學機械工程研究所碩士論文,1996
11.葉維磬,吳仲育, "應用流函數法分析通過曲線模之軸對稱擠製之上界限解" 中華民國第十八屆全國力學會議, pp.153-161, 1994.
12.吳明昌, "應用流函數法分析軸對稱熱擠製加工問題." 國立中央大學機械工程研究所碩士論文,2000
13."Element Library," MARC Analysis Research Corporation. Volume B. Version K7. pp.2.6-2.8
14.Shiro Kobayashi, Soo-Ik Oh, Taylan Altan, " Metal Forming and the Finite-Element Methed," pp.90-110, Oxford university Press, 1989.
15.Hibbitt H.D., Marcal P.V. and Rice J.R. "A Finite Element Formulation for problems of large strain and large displacement.", Int. J. Soilds Struct. Vol.6, 1970, pp.1069-1086
16.Mcmeeking R.M. and Rice J.R., "Finite Element Formulation for Problem of Large elastic-plastic deformation.", Int. J. Soilds struct., Vol.11, pp.601-616.
17."Mentat Command Reference," MARC Analysis Research Corporation. Version 3.1, pp. 3-345~3-350.
18."Theory and user information," MARC Analysis Research Corporation. Volume A. Version K7.
19."Mentat Command Reference," MARC Analysis Research Corporation. Version 3.1.
20.Lee, G. A, Im, Y. T., " Finite-element investigation of the wear and elastic deformation of dies in metal forming," Journal of Materials Processing Technology, pp. 123-127, 1999.
21.Archard, J. F., J. Appl. Phys. 24 pp.981. 1953.
22.Lee, H. I., Hwang, B. C, Bae, W, B.," A UBET analysis of non- axisymmetric forward and backward extrusion," v.113 n.1 pt.0 pp.103-108, 2001.
23.Chanda, Tapas, Zhou, Jie, Duszczyk, Jurek "A comparative study on iso-speed extrusion and isothermal extrusion of 6061 Al alloy using 3D FEM simulation," Journal of Materials Processing Technology, Vol. 114, pp. 145-153, 2001.
24.江卓培﹐”漸開線外齒輪鍛造之有限元素分析”﹐碩士論文﹐國立中央大學機械所﹐1999
25.何信森﹐”方杯引伸成形之彈塑性有限元素分析”﹐碩士論文﹐國立中央大學機械所﹐1999