基于哈密顿理论的薄壁结构双向弯曲分析

摘要

Based on the energy variation principle, dual variables are introduced by the Legendre's transformation.Hamiltonian dual systems are presented for the bending problems of thin-walled structure.Control differential equations of the thin-walled structure were transformed into Hamiltonian dual equations.Numerical calculation has good stability because the system matrix has characteristics of the symplectic matrix,then numerical solutions with high accuracy are often obtained with the precise integration method.The results of the example show that the method has higher precision and applicability.Moreover,it can be applied conveniently to calculating problem of non-uniform thin-walled structure.%从能量变分原理出发,由勒让德变换引入对偶变量,导出了薄壁结构双向弯曲问题的哈密顿对偶求解体系,将薄壁结构的控制微分方程转化为哈密顿对偶方程,其系统矩阵具有辛矩阵的特性,可用精细积分法求该体系的高精度数值解.算例计算结果表明,本方法具有较高的精度和适用性,并可方便地用于变截面薄壁结构的计算.