Improvements Of 8-node Biquadratic Q8-element By Hybrid/Combined Hybrid FEMS

There are disadvantages of sensitivity to mesh distortions and Poisson-Lockingfor 8-node isoparametric biquadratic Q8-element, which applied widely in engi-neering finite elements. Two hybrid stress finite element methods were proposedto remove disadvantages, while improving the accuracy. Extrapolation methodwas also used to recover the locking stress of Q8.We got two new finite elements: CH9β(α) and HS13β. The isoparamet-ric biquadratic displacements interpolation of Q8-element is used in two ele-ments. CH9β(α) is based on the combined hybrid variational principle, and a9-parameter linear stress mode is used. HS13βis based on the Hellinger-Reissnervariational principle, and a 13-parameter stress mode is used. The convergence isensured by theory analysis. Numerical tests indicate that the new methods havebetter numerical accuracy than Q8, are insensitive to mesh distortions and freeof Poisson-Locking. Due to elimination of stress parameters at the element level,the methods are of the same computational cost as Q8-element.There are always stress locking, while more precise displacement, in PoissonLocking. Extrapolation method was used to recover stress of Q8, and got betterstress accuracy.