Abstract: The 9node isoparametric element of Hamiltonian canonical equation has been established by combining the modified HellingerReissner (HR) variational principle of elastic material and quadratic interpolation function of 9node quadrilateral isoparametric element. Firstly, the modified HR variational principle for the elastic material was briefly presented. Then, based on the variational principle and the 3×3 Guass integration, the Hamilton canonical equation of 9node isoparametric element was derived in detail. The advantages of 9node isoparametric element in finite element were combined with the semianalytical method of elasticity Hamilton canoncial equation organically. The results of numerical examples prove the correctness of the 9node isoparametric element formulation.

Key words: Hamilton canonical equation; 9node isoparametric element; semianalytical method; Gauss integral