Hamilton正则方程半解析法的收敛和对称分析

近年来,Hamilton正则方程半解析法在工程问题上的应用越来越广泛,但至今未见有关这种方法收敛性和对称性问题研究的文献。基于Hamilton正则方程的半解析法理论,通过变分原理详细推导了Hamiltonian元素的固支和简支边界公式及对称边界公式。多个实例的数值研究表明：随着网格加密,Hamilton正则方程半解析法的收敛速度快于一般传统位移有限元法,对称解法的效率明显优于整体解法。

Convergence and Symmetry Analysis for Semi-Analytical Solution of Hamilton Canonical Equation

The semi-analytical solution for Hamilton canonical equation is employed widely in the engineering problems in recent years. However,authors still do not find the relevant references on convergence and symmetric problems of the semi-analytical solution. Based on the semi-analytical solution for Hamilton canonical equation theory,the formulations of the clamp and simply supported and symmetric boundary conditions on the Hamiltonian element are derived by the variational principle. Several numerical examples show that with increase of meshes ,the convergence rate of the semi-analytical solution is faster than the convergent rate of traditional finite element method based on displacement. The operation efficiency of symmetry solution is obviously priors to whole solution.