基于切应力条件的广义协调等参元

A Generalized Conforming Isoparametric Element Under Shear Stress Field

非协调位移模式可有效改善计算精度,但对任意非规则网格常不能满足收敛性条件.根据线性边界力状态下的广义协调条件,对任意不规则四边形单元构造出一种广义协调等参元.该单元的导出考虑了线性切应力条件,使单元间位移协调条件在加权残数意义上得以满足.进一步给出了相应的广义协调应变形函数矩阵,模式紧凑而不易出现奇异性.该等参元对任意不规则四边形网格能通过分片检验,当单元为平行四边形时蜕化为Q6元.算例表明,该类型等参元精度较高,对不规则网格剖分能保持良好的数值性态.

<Abstrcat> The numerical precision can be effectively improved by non-conforming displacement, but the convergence criteria is not satisfied for the non-conforming quadrilaterals for arbitrary irregular mesh often.A new generalized conforming isoparametric element is formulated to arbitrary irregular quadrilateral for plane stress analysis.Under linear shear stress field, generalized compatibility condition is presented. In the sense of weighted residual ,the displacement is satisfactory to compatibility. And further, strain shape function matrix is given with generalized conforming modes. As compared with some existing others, the element can pass the patch test for arbitrary irregular mesh. When it is a parallelogram the element degenerates to Q6. Numerical examples show that the element is less sensitive to geometric distortion and the result is better.