反向NQ6非协调元

REVERSE ADJUSTMENT OF NON-CONFORMING ELEMENT NQ6

为通过强式分片试验,NQ6单元对Q6单元的非协调内部形函数进行了线性修正,但抗畸变性能下降了.论文提出对线性修正项进行反向调整以恢复甚至提高抗畸变性能.调整过程是把线性修正项看成影响单元性能的一维方向,进行反向搜索确定有利的计算步长.进行了典型算例测试,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时新单元的畸变敏感性优于原Q6、NQ6,特别地在-2附近可有效消除剪切闭锁;除弱式分片试验外,总体性能和精度达到或接近各类4节点四边形单元的最好水平.

To pass the strong-form patch test,element NQ6 introduced additional linear items into the internal non-conforming shape functions of element Q6 at the cost of an anti-distortion performance degra- dation. This study was focused on how to resume and even improve the anti-distortion performance, through which a reverse adjustment method was proposed during the handling of these linear modifica- tions. First, the additional linear item of each internal shape function was treated as a one-dimensional direc- tion that influences the anti-distortion performance of the element. A reverse search was then performed to determine the favorable step size by means similar to the advance and retreat method of optimization. Some typical examples were tested,the results of which showed that the reverse adjustment was effective. With the adjustment factor set as the mirror value,--1, and further extended to --2, the newly obtained elements were less sensitive to distortion than the original Q6 and NQ6. In particular,it was found that the shear loc- king in MacNeal slender beam was efficiently eliminated when the value was around --2. Because of the re- verse treatment, the new elements only passed the strong-form patch test with parallelogram mesh. Except for this,the overall performance and accuracy was close to the best of various 4-node quadrilateral ele- ments. Obtaining additional items of the internal shape functions by strong-form patch test with reverse ad- justment,the proposed method suggested a new way in improving the anti-distortion performance of the Q6-type non-conforming elements.