广义协调等参元
A Generalized Conforming Isoparametric Element
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摘要: 本文根据广义协调条件,对平面应力四边形单元提出一个广义协调等参元GC-Q6.单元GC-Q6是对Wilson非协调等参元Q6的一个改进方案:单元Q6只对平行四边形网格情况能通过分片检验,对一般四边形情况却不能通过,而本文的单元GC-Q6则对一般四边形情况也能通过.当单元为平行四边形时,GC-Q6单元即退化为QS单元.算例表明,广义协调等参元的应力精度高于文献中已有的单元,对不规则网格均能保持良好的性态.Abstract: Based on the generalized compatibility condition under constant and linear stress field, a quadrilateral generalized conforming isoparametric element, GC-Q6, for plane stress analysis, is developed. The element GC-Q6 can be regarded as an improved form of Wilson's non-conforming isoparametric element Q6. GC-Q6 can pass the patch test for arbitrary irregular mesh while Q6 can not. GC-Q6 degenerates to Q6 when it is a parallelogram. Numerical examples show that the GC-Q6 element gives more accurate stress solution than the existing non-conforming elements and is less sensitive to geometric distortion.
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[1] Wilson, E.L., et al., Incompatible displacement models, Numerical and Computer Methods in Structural Mechanics, ed. Fenves S.J., et al., Academic Press, New York(1973), 43-57. [2] Taylor, R.L., et al., A non-conforming element for stress analysis, Int. J. Num. Meth. Engng., 10(1976), 1211-1219. [3] Wachspress, E.L., Incompatible quadrilateral basis functions, Int. J. Num. Meth. Engng., 12(1978), 589-595. [4] 陈万吉、唐立民,等参拟协调元,大连工学院学报,20, 1 (1981), 63-74 [5] Pian, T.H.H. and Wu Chang-chun, General formulation of incompatible shape function and an incompatible isoparametric element, Proc. of the Invitational China-American Workshop on FEM, Chengde, China, June 2-6(1986), 159-165. [6] 龙驭球、辛克贵,广义协调元,土木工程学报,20(1987),1-14. [7] Cook, R.D., Improved two-dimensional finite element, J. Struct. Div., ASCE, 100. ST9(1974), 1851-1863. -
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