Abstract
The element-free method is a new numerical technique presented in recent years. It uses the moving least square(MLS) approximation as its shape function, and it is determined by the basic function and weight function. The weight function is the mainly determining factor, so it greatly affects the accuracy of the computational results. The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation. The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot. Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained. The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts.
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References
ZHOU Wei-yuan, KOU Xiao-dong. Element-free method and its application in engineering [J]. Acta Mechanica Sinica, 1998, 30(2): 193–202. (in Chinese)
ZHANG Xiong, LIU Yan. Meshless method [M]. Beijing: Tsinghua Press, 2005: 1–2. (in Chinese)
CHUNG H J, BELYTSCHKO T. An error estimate in the EFG method [J]. Computational Mechanics, 1998, 21: 91–100.
BELYTSCHKO T, ORGAN D, KRONGAUZ Y. A coupled finite element-element-free Galerkin method [J]. Computational Mechanics, 1995, 17: 186–195.
LONG Shu-yao, HU De-an. A study on the weight function of the moving least square approximation in the local boundary integral equation method [J]. Acta Mechanica Sinica, 2003, 16(3): 276–279.
LIU G R, TU Z H. An adaptive procedure based on background cells for meshless methods [J]. Comput Methods Appl Mech Engrg, 2002, 191: 1923–1943.
XIAO Q Z, DHANASEKAR M. Coupling of FE using collection approach [J]. Engineering Software, 2002, 33: 507–512.
TIMOSHENKO S P, GOODIER J N. Theory of elasticity (3rd ed) [M]. New York: McGrawHill, 1987.
YIN Shui-ping, LUO Ying-she, CAO Zheng, LIU Wen-bin. Study on weight functions efficiency of element-free Galerkin method [J]. National Science Journal of Xiangtan University, 2007, 29(3): 65–70. (in Chinese)
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Foundation item: Key project(02103) supported by National Education Department of China; Key project(02A008) supported by the Education Department of Hunan Province, China; Project(2005090) supported by Central South University of Forestry and Technology; Project(03JJY3007) supported by the Natural Science Foundation of Hunan Province, China; Project supported by the Rewarding Project for Excellent PhD Thesis of Hunan Province, China; Project(07031B) supported by Scientific Research Fund of Central South University of Forestry and Technology
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Luo, Ys., Yin, Sp. & Yu, M. Application in metal rheological forming of element-free Galerkin method. J. Cent. South Univ. Technol. 15 (Suppl 1), 187–191 (2008). https://doi.org/10.1007/s11771-008-0343-x
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DOI: https://doi.org/10.1007/s11771-008-0343-x