反向Qm6非协调元

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。

Reverse adjustment of non-conforming element Qm6

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.