| 胡圣荣,许静静,刘新红.反向Qm6非协调元[J].计算力学学报,2016,33(6):932~937 |
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| 反向Qm6非协调元 |
| Reverse adjustment of non-conforming element Qm6 |
| 投稿时间：2015-07-22 修订日期：2015-11-12 |
| DOI：10.7511/jslx201606020 |
| 中文关键词: 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 |
| 英文关键词:non-conforming element patch test distortion sensitivity element Q6 element Qm6 4-node quadrilateral element |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| Element Qm6 drops its anti-distortion performance due to especial numerical treatment applied to Q6's matrix [G] 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 advantage. |
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