八节点Hamiltonian等参元列式

为了使平面八节点等参元的优越性在弹性力学Hamilton正则方程的半解析法得到应用。结合弹性材料修正后的Hellinger—Reissner（H—R）变分原理和二次插值函数表达平面外应力和位移函数，建立了Hamilton正则方程的八节点等参元列式。首先简要地介绍了弹性材料修正后的H—R变分原理．然后用二次插值函数表示平面外应力和位移变量，并详细地推导了Hamilton正则方程的八节点等参元列式。数值实例结果证明了本文等参元列式的正确性。

8-Node Isoparametric Element for Hamiltonian Canonical Equation

In order to combine the advantages of 8-node isoparametric elements with a semi-analytical solution of Hamilton canonical equation, the formulation of isoparametric element with 8-node for Hamilton canonical equation was presented in this paper by combining the modified Hellinger-Reissner （H-R） variational principle for elastic material and out-plane stress ＆ displacement variables in quadratic interpolation functions forms. Firstly, the modified H-R variational principle for elastic material was briefly presented, then the quadratic interpolation functions were used to express the out-plane stresses and displacements variables, consequently the formulation of 8-node isoparametric element for Hamilton canonical equation was derived in detail. The results of numerical examples show the correctness of present formulation of isoparametrie elements.