反向Qm6非协调元  

Reverse adjustment of non-conforming element Qm6

作　　者：胡圣荣[1] 许静静[1] 刘新红[1] 

机构地区：[1]华南农业大学工程基础教学与训练中心,广州510642

出　　处：《计算力学学报》2016年第6期932-937,共6页Chinese Journal of Computational Mechanics

摘　　要：为通过强式分片试验,Qm6单元对Q6单元非协调部分的[G]矩阵进行了特殊的计算处理,但抗畸变性能下降,本文提出对有关处理反向进行,以恢复甚至提高抗畸变性能。分析了Qm6单元的原理,指出其实质是修改雅可比矩阵[J]的伴随矩阵[J*],在非协调部分[G]矩阵的计算时,把[J*]看成可变量,由Qm6的对应点向Q6方向进行反向搜索,查找有利的计算点。进行了典型和苛刻的算例测试,结果表明反向调整是有效的,调整系数取镜像值-1以及扩展到-2时,新单元的抗畸变性能优于原Q6和Qm6,其中取-2对消除剪切闭锁是最优点;除弱式分片试验外,总体性能和精度接近各类4节点四边形单元的最好水平。由于方法和原理简便,实现以及推广到三维问题都有显著优势。Element Qm6 drops its anti-distortion performance due to especial numerical treatment applied to Q6＇s matrix I-G3 of nonconforming items when forcing strong patch test. It is proposed to carry out reverse treatment on element Qm6 to resume and even improve the anti-distortion performance. By analyzing the principle of Qm6 ,it is pointed out that such principle is essentially to modify adjoint matrix [ J＊] of Jacobian matrix [J＊] , so in calculating nonconforming items＇ matrix [G], it is suggested to take [J＊] as a variable, do reverse searching along the direction from the corresponding point of Qm6 to that of Q6 for favorable calculation position. Some typical and harsh examples are tested; results show that the reverse treatment is effective, with adjustment factor set to mirror value -1,and further extended to -2,the resulting elements are less sensitive to distortion than the original Q6 and Qm6, especially the value -2 is optimal for elimination of shear locking. Except for weak patch test,the overall performance and accuracy are close to the best of various 4-node quadrilateral elements. With the simplicity of the method and principle, the implementation and generalization to 3D problems have a significant advan- tage.

关 键 词：非协调元 分片试验 畸变敏感性 Q6单元 Qm6单元 4节点四边形单元 

分 类 号：O242.82[理学—计算数学]