横向加强构件作用下的开口薄壁梁等效建模方法

卫星结构中通常有大量横向加强构件作用下的开口薄壁杆件，横向加强构件一般沿杆件轴向均匀分布，通过对这类结构研究，理论上证明了这种结构的振动微分方程与普通的开口薄壁梁振动微分方程有相同的形式，因此可以用开口薄壁梁单元进行等效计算。本文建立了开口薄壁梁的3种数学模型：有限元模型、传递矩阵模型和解析模型。采用优化理论中序列二次规划对等效截面参数进行辨识，同时分析了不同目标函数对辨识结果的影响，并且提出了一种对截面初始参数进行估计的方法。对于有限元模型，提出采用MATLAB与ABAQUS交互式参数优化方法，充分结合二者优点可以快速高效地对截面参数进行优化辨识，具有较强的通用性。通过实验验证了这种等效建模方法的正确性与精确性。所提出的等效建模方法可以减少90%以上的单元数量。通过建立这种简化模型，可以大幅度提高整星结构模型修正与结构重分析的效率。

Equivalent modeling method of open thin-walled beam under action of transverse stiffening member

Satellite structures usually have a lot of open thin-walled beams under the action of transverse stiffening member. Transverse member is generally evenly distributed along the axial direction of the beam. Through the study of such structures, it is theoretically proved that the differential equation of vibration of this structure has the same form as the equation of ordinary open thin-walled beam. Therefore, equivalent calculation was carried out using the open thin-walled beam element. Three kinds of mathematical models of open thin-walled beams, finite element model, transfer matrix model and analytical model, were established. The equivalent cross-section parameters were identified using sequential quadratic programming. At the same time, the influence of different objective functions on the identification results was analyzed. And a method for estimating the initial parameters of the cross-section was presented. For the finite element model, the MATLAB and ABAQUS interactive parameters optimization method was proposed. A combination of both full advantages can quickly and efficiently optimize the cross-section parameters and this method has strong versatility. Finally, the correctness and accuracy of the equivalent modeling method are verified by experiments. The proposed equivalent modeling method can reduce more than 90% of the number of elements. By establishing the simplified model, the efficiency of the structural model updating and structure reanalysis can be greatly improved.