本研究使用有限元素分析軟體ANSYS，使用雙橢圓移動熱源，以元素的生與死技術模擬三維單V形槽之對接銲，重現銲料的填入過程，並比較在不同之單V形槽角度之條件下其溫度場、應力場與角變形量之差異。
對於溫度場的分析，研究結果顯示對於有開槽角度的銲接方式，使用體熱源比表面熱源之熔融區較接近實際銲接情況。且由熱循環曲線圖可以看出，銲道中之元素於銲接熱源到達時才升溫，與實際有填充金屬銲接情況相同，因此使用元素的生與死方法較符合實際銲接的溫度變化情形。
在應力場的研究中，由於銲道金屬於填入銲道時處於熔點，此時並無應力應變存在，因此利用元素的生與死技術使模型中尚未填入銲道之元素與銲道中高於熔點的元素不發生作用，待低於熔點時才啟動元素參與應力計算，於殘留應力分析時，殘留應力之分佈與實驗之趨勢吻合。
對於有開槽角度之角變形分析，研究結果顯示如直接於銲道施加熱量，角變形方向將與實際結果相反。本研究採用元素的生與死技術，並且定義計算銲道元素熱應變之參考溫度為熔點溫度，使得銲道於熱通量施加時不產生膨脹變形，模擬角變形方向與實際變形方向一致，而角變形量會隨單V形槽角度增加而增加，與實驗結果相同。

Welding is used in industry in a broad number of ways. In the past, in order to measure welding temperature fields, stress fields and deformation, one had to conduct a physical experiment. Unfortunately, conducting experiments has many restrictions such as budget, time, and the requirement of a large amount of labor. However, with the use of the finite element method in the welding process, one can quickly forecast welding temperature fields, stress fields and deformation.
The calculation in the welding process is a nonlinear procedure in which the material properties change with the temperature. Furthermore the analytical results of the temperature fields adjacent to the heat source are rather steep. The problem of the fusion and solidification of material has been solved by the method of “Element Birth and Death”, and the thermal stress and residual stress in welding can be predicted by using the simulative analysis method.
In this paper, heat flux is modeled with double ellipsoid heat source model, a feasible dynamic simulation method on 7075 Al alloy’s 3D welding temperature fields, stress fields has been established, which provides theory foundation and instruction on optimizing the welding technology and parameters.
Single V-groove butt welding on three types of heat treatable aluminum alloys 7075-T6 and compared the angular distortion levels of the aluminum alloys at different Vee preparation angles. Simulations of the angular distortion by the reference temperature of the melting point on fusion volume for the thermal strain calculations have been used, and the results demonstrated the single Vee preparation angle (amount of filler metal) in butt welding affected the angular distortion of the weldment. The angular distortion tended to increase with the single Vee preparation angle.

參考文獻
[1] 謝元峰，基於ANSYS的焊接溫度場和應力的數值模擬研究，武漢理工大學碩士論文，西元2006年4月。
[2] Paley, Z., Hibbert, P.D., Computation of temperatures in actual weld designs, Welding Journal, 54(11):385–392, 1975.
[3] Wang J., et al., Improvement in numerical accuracy and stability of 3-D FEM analysis in welding, Welding Journal, 75 (4):129-134, 1996.
[4] Wang J., et al. An FEM model of buckling distortion during welding of thin plate, J. of Shanghai Jiaotong University, E.4 (2):69–72, 1999.
[5] Tall, and L., Calculation of residual stresses in perspective, IEEE Transactions on Nuclear Scienc, 49–62, 1978.
[6] Jaroslav and Mackerle, Finite element analysis and simulation of welding—an addendum: a bibliography (1996–2001), Modelling Simul. Mater. Sci., Eng. (10), 295–318, 2002.
[7] K. Asubuchi, Prediction and control of residual stresses and distortion in welded structures, Proc. Theoretical Prediction in Joining and Welding, Osaka, Japan, 71–88, Nov. 1996.
[8] K. S. Alfredsson and B. L. Josefson, Harmonic response of a spot welding box beam influence of welding residual and deformations, Proc IUTAM Symposium on the Mechanical Effects of welding LILEA, Sweden, 1–8, Jun. 1991.
[9] Shim, Y., Feng, Z., Lee, S., et al., Determination of residual stresses in thick-section weldments, Welding Journal, 71(9):305–312, 1992.
[10] J. Goldak, et al.. Thermal stress analysis of welds: from melting point to room temperature, Proc. Theoretical Prediction in Joining and Welding, Osaka, Japan, 225–230, Nov. 1996.
[11] L. Karlsson. et al., Thermal stresses in welding, in R. Hetnarski (ed.). Thermal Stresses I, North. Holland, Amsterdam, Chapter 5, 1986:299–389
[12] Bachorski, A., and Painter, M.J., et al., Finite-element prediction of distortion during gas metal arc welding using the shrinkage volume approach, Journal of Materials Processing Technology, 92-93(30):405–409, 1999.
[13] Teng Tso-Liang, Fung Chin-Ping, Chang Peng-Hsiang, Yang Wei-Chun, Analysis of residual stresses and distortions in T-joint fillet welds. Int J Pressure Vessel Piping, 78:523–38, 2001.
[14] Fanous FZ Ihab, Younan, Maher YA, Wifi S Abdalla, 3-D Finite element modeling of the welding process using element birth and element movement techniques, Tran ASME J Pressure Vessel Technol, 125:144–50, 2003.
[15] D. Berglunda, et. al., Simulation of welding and stress relief heat treatment of an aero engine component, Finite Elements in Analysis and Design, 865–881, 2003.
[16] G Casalino, S J Hu and W Hou, Deformation prediction and quality evaluation of the gas metal arc welding butt weld, Proceedings Institution of Mechanical Engineers, Part B: J. Engineering Manufacture, Vol. 217, 2003.
[17] D. Gupta, and K. Kim, Welding distortion minimization for an aluminum alloy extruded beam structure using a 2D model, Vol. 126, Feb. 2004.
[18] M.M.Mahapatra et al., Three-dimensional finite element analysis to predict the effects of SAW process parameters on temperature distribution and angular distortions in single-pass butt joints with top and bottom reinforcements, International Journal of Pressure Vessels and Piping, 721–729, 2006.
[19] Q.G. Meng et. al., Theoretical and Applied Fracture Mechanics 44, 178–186, 2005.
[20] Z. Dong and Y. Wei, Three dimensional modeling weld solidification cracks in multipass welding. Theoretical and Applied Fracture Mechanics, 156–165, 2006.
[21] L. Yu-cheng, Y. Wen-xia, and L. Cai-hui, et. al., Simulation on temperature field of TIG welding of copper without preheating, Transactions of Nonferrous Metals Society of China.
[22] R. Spina, L. Tricarico, and G. Basile, et. al., Thermo-mechanical modeling of laser welding of AA5083 sheets, Journal of Materials, Processing Technology, 215–219, 2007.
[23] 曾光宏，不銹鋼銲件變形與殘留應力之研究，國立交通大學機械工程研究所博士論文，西元2000年。
[24] 鄭慶民，熱處理型鋁合金銲接性之研究，國立交通大學機械工程研究所博士論文，西元2005年5月。
[25] Saeed, Moaveni., Finite Element Anlysis – Theory and Application with ANSYS
[26] 薛忠明，金屬構件熔化焊接熱力分析與模擬研究，北京航空航天大學博士學位論文，西元2003年8月。
[27] Pavelic, V., Tanbakuchi, R., Uyehara, O.A., et al., Experiment and computed temperature histories in gas tungsten-arc welding of thin plates. Welding Journal, 48(7):295–305, 1969.
[28] Chong L.M. Predicting welding hardness[D]. M, Eng, Thesis. Ottawa, Canada: Carleton University, 52–57, 1982.
[29] X.K. Zhu, Effects of temperature-dependent material properties on welding simulation, Computers and Structures, (80)967–976, 2002.
[30] D. Berglund, H. Alberg, H. Runnemalm, Simulation of welding and stress relief heat treatment of an aero engine component, Finite Elements in Analysis and Design, (39)865–881, 2003.
[31] ASM Handbook: Formerly Tenth Edition, volume 2 Properties and Selection: Nonferrous Alloys and Special-Purpose Materials
[32] METALS HANDBOOK, Desk Edition, Edited by Howard E.boyer, Timothy L.Gall, AMERICAN SOCIETY FOR METALS
[33] 黃伯元等主編，中國材料工程大典，第四卷，有色金屬材料工程(上)，西元2005年8月。
[34] "Welding Technology", Welding Handbook: eight edition, vol. 1, AWS, 1987.
[35] 吳聖川，鋁合金激光-電弧複合焊研究及其溫度場的數值模擬，華中科技大學，碩士論文，西元2005。
[36] 李東林，焊接應力和變形的數值模擬研究，武漢理工大學，碩士論文，西元2003年3月。
[37] John Goldak, A new finite model for welding heat source, Metallurgual. Transactions, 15B(2):299–305, 1984.
[38] Chong L.M. Predicting welding hardness[D]. M, Eng, Thesis. Ottawa, Canada: Carleton University, 1982, 52–57
[39] Thermo-mechanical modeling of laser welding of AA5083 sheets, Journal of Materials Processing Technology, 2007, (191) 215–219
[40] C D Jang, C H Lee and D E Ko, Prediction of welding deformations of stiffened panels, Engineering for the Maritime Environment, 135, 2002.
[41] 梁曉燕，中厚板多道焊焊接過程中溫度場和應力場的三維數值模擬，華中科技大學，碩士論文，西元2004年。
[42] 謝元峰，基於ANSYS的焊接溫度場和應力的數值模擬研究，武漢理工大學，碩士論文，西元2006年4月。
[43] 蔡宗亮，銲接應力與變形，銲接工程技術研習會論文集，1985。