组合断面薄壁杆件弯扭耦合分析

BENDING-TORSION COUPLING ANALYSIS OF THE COMPOSITE SECTION THIN-WALLED BAR STRUCTURE

根据薄壁杆件结构约束扭转的一致性理论,研究了由多个薄壁杆件组成的组合薄壁杆件结构的弯扭耦合问题。在符拉索夫刚周边假定,库尔布鲁纳-哈丁理论对纵向翘曲位移的假定和弯曲时的平截面假定下,得到了弯扭耦合作用下组合断面薄壁杆件结构的总势能,并由此得出相应的拉格朗日函数。引入对偶变量,建立了组合断面薄壁杆件结构静力分析的哈密顿对偶体系,导出了弯扭耦合分析的哈密顿正则方程。用两端边值问题的精细积分法可求出高精度数值解。这种方法适合于开口断面、闭口断面及开闭口混合断面薄壁杆件结构的弯扭耦合分析。该方法是哈密顿力学在组合断面薄壁杆件结构弯扭耦合分析中的应用,数学推导过程简单,且有成熟高效的数值算法,思路清晰、精度高、易于接受。

Based on the consistency theory of restrained torsion, the coupled bending-torsion problem of composite section thin-walled bar structures consisting of some thin-walled bars is studied in this paper. The total potential energy of thin-walled bar structure with bending-torsion coupling and its corresponding Lagrange function are obtained on the basis of Vlasov’s rigid-frame assumption, Kollbrunner-Hajdin’s longitudinal warping displacement assumption and the plane-section assumption of bending. By introducing dual variables, a Hamiltonian dual system for the static analysis of a composite section thin-walled bar structure is constituted, then Hamiltonian canonical equations are derived for the analysis of bending-torsion coupling. High accuracy numerical solutions are obtained using a precise integration method of two end boundaries. The method proposed in this paper is applicable for the bending-torsion coupling analysis of thin-walled bar structures of open sections, closed sections and mixed sections. And it is the application of Hamiltonian mechanics in the bending-torsion coupling analysis of a composite section thin-walled structure. It is highly accurate and easy to accept with a simple and clear mathematic derivation as well as efficient numerical algorithms.