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显式辛数值算法有一个重要的特性,即在长时间内保存Hamilton函数的指数幂,用这种方法求解可分的微分方程所得到的解逼近精确解。该文基于压电材料修正后的H-R混合变分原理,首先推导了Hamiltonian四节点有限元列式,然后通过对该列式进行行列变换,得到了K正则方程。最后将显式辛数值算法用于求解压电材料层合板的静力学问题,数值算例说明显式辛数值算法完全可以应用到高维的微分方程中。
The explicit symplectic numerical algorithm has an important property of preserving the exponential power of the Hamiltonian function over a long period of time and using this method to solve the exact solution of the solution to the separable differential equations. Based on the H-R mixed variational principle modified by piezoelectric materials, the Hamiltonian four-node finite element method is deduced first. Then, the K-regular equations are obtained by the column and column transformation. Finally, the explicit symplectic numerical algorithm is used to solve the statics problem of the piezoelectric material laminate. Numerical examples show that the explicit symplectic value algorithm can be applied to high-dimensional differential equations.