带有摩擦的单边接触大变形问题的研究(Ⅱ)——非线性有限元解及应用
On Unilateral Contact Large Deformation Problem with Friction——(Ⅱ) Nonlinear Finite Element Technique and Its Application
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摘要: 在文[1]所建立的增量变分力程的基础上,本文建立了单边接触弹塑性大变形问题的非线性有限元增量方程;进一步阐述了基于拖带坐标系的大变形有限元方法的特点,建立了实用的大变形接触模型.作为应用实例,计算了悬臂梁、厚圆板的弹性接触大变形和金属圆环弹塑性接触大变形问题,得到了令人满意的计算结果.Abstract: Based on the variational equation derived in ref.[1], a nonlinear incremental F.E. equation is formulated for unilateral contact elastic and plastie large deformation problems. A new technique-co-moving coordinate finite element method is introduced, and a practical mathematical model for large deformation contact problem is described. To show the effectiveness of the method, problems of contact large deformation of cantilever bean, circular plate, as well as metal ring are computed. Compared with experiments, the results show good agreements.
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[1] 尚勇、陈至达,带有摩擦的单边接触大变形问题的研究(I)一增量变分方程,应用数学和力学.1,12(1989),1049-1058. [2] Reddy,T.Yella and S.R.Reid,Phenomena associated with the crushing of metal tubes between rigid plates,Int.J.Solids and Struct.,16(1980),545-562. [3] Taylot,L.M.and E.B.Backer,Some computational aspects of large deformation,rate-depelldent plasticity problems,Comp.Meths.Appl.Mech.Eng.,41(1983),251-278. [4] Oden.J.T.and G.F.Carey,Finite Element.Vol.Ⅴ,Prentice-Hall,Inc.(1984). [5] 陈至达,《有理力学》、中国矿业大学出版社(1988). [6] 尚勇、带有接触摩擦边界弹塑性大变形问题的理论和有限元分析.中国矿业大学博士学位论文(1987). [7] 尚勇、陈至达,论拖带坐标系中应力的客观速率,应用数学和力学,10,2 (1989),85-104. [8] Neale,K.W.,Phenomenological constitutive laws in finite plasticity,SM Archives,6(1981),79-129. [9] Shang Yong(尚勇) and Chen Zhi-da(陈至达),Analysis of large elastic-plastic deformation by finite element method using co-moving coordinate,Proc.ICNM,Shanghai(Ed by Chien Wei-zang(钱伟长)),Science Press(1985),1294-1301. -
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