平面杂交动态有限元法

2-Dimension Dynamic Hybrid/Mixed Element Method

本文从Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ泛函出发，以应力和位移作为独立的场变量，给出了平面杂交／混合动态有限元法的一般列式。克服了用杂交应力法求解结构动力问题时的泛函不一致性。同时，简化了Ｋ．Ｋ．Ｇｕｐｔａ提出的一维、二维动态有限元法（ＤＥＭ）的列式，便于计算机统一实施。根据本文方法，计算了平面悬臂方板的自由振动频率。结果表明，本文方法合理、有效。

Based on the Hellinger-Reissner variational formulation with stress and displacement as indepdent variables,a generalized formulation of Dynamic Hybrid/Mixed Element Method(DHEM)for 2-Dproblems is presented.The contradiction of inconsistency encountered in the conventional hybrid stress modelling,in dynamic analysis,can be avoided.Furthermore,the formulation of Finite Dynamic Element Method(DEM)for 1-Dand 2-Dproblems can be simplified and computer implementation is convenient.Numerical results of free vibration analysis for cantilever plate clearly indicate that the present DHEM provides the most economical and efficient solution for such an analysis when compared with the usual FEM and DEM.