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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。
According to the consistence theory of thin-walled bars, the problem of the torsional-torsional coupling of the thin-walled thin-walled bars with multiple thin-walled bars is studied. Based on the assumption just around the Furasov, the assumption of the longitudinal warp displacement and the assumption of the flat section under bending in the Kühlulühlud-Harding theory, the total sectional structure of the thin-walled rod with combined section under bending and torsional coupling is obtained. Potential energy, and draw the corresponding Lagrange function. By introducing the dual variables, the Hamiltonian dual system of the static analysis of composite thin-walled section structures is established, and the Hamiltonian equations of bending-torsional coupling analysis are derived. The precise integration method with two-end boundary value problem can be used to obtain high-precision numerical solution. This method is suitable for the bending-torsion coupling analysis of the thin-walled bar structure with open section, closed section and open-close mouth. The method is applied to the analysis of bending-torsion coupling of thin-walled bar structure with combined section. The method of mathematical derivation is simple and has a mature and efficient numerical algorithm with clear ideas, high precision and easy acceptance.