矩形箱梁约束扭转分析的精细积分法

Precise integration method of restrained torsion analysis of rectangular box shaped beam

在薄壁杆件结构约束扭转的一致性理论前提下,以断面的扭角φ(z),翘曲θ(z)为基本未知函数,引入相应的对偶变量,建立了矩形箱梁约束扭转问题的哈密顿对偶求解体系,导出了问题的控制方程(哈密顿正则方程)。方程中的系统矩阵具有辛矩阵的特性,能方便地通过精细积分法求出高精度数值解。该方法是哈密顿力学在薄壁杆件结构约束扭转分析中的应用,数学推导简单,且有成熟高效的数值算法,思路清晰、精度高、易于接受,对问题的求解提供了新的思路。

Under the premise of the consistency theory of the thin-walled bar＇s restrained torsion, the torsional angle φ （z） and warp θ （z） of the section are taken as the primary unknown functions. By introducing dual variables,Hamihonian dual system for the analysis of restrained torsion of rectangular box shaped beam is constituted, then control equations （ Hamihonian canonical equations） of the problem are derived. The system matrix in the equations has characteristics of the symplectic matrix,then numerical solutions with high accuracy are often obtained with the precise integration method. And it is the application of Hamiltonian mechanics in the restrained torsion analysis of thin-walled structure. It is hightly accurate and easy to accept with a simple and clear mathematic derivation as well as efficient numerical algorithms. It supplies a new way to solve problems.