拱形温室纵向抗风分析中的曲梁刚度矩阵模型

Curved beam stiffness matrix model for longitudinal wind resistance analysis of arch greenhouse

关键词:  拱形温室  纵向抗风  曲梁  弯扭耦合  刚度矩阵

Key words:  arch greenhouse  longitudinal wind resistance  curved beam  bending-torsion coupling  stiffness matrix

摘要:

为研究拱形温室纵向抗风分析中的屋面拱结构，考虑弯扭耦合的影响，在对其几何方程、平衡方程、物理方程分析的基础上，建立了曲梁扭转角和弯曲挠度的控制方程；求得了用基函数向量以及积分常数向量表达的曲梁扭转角和弯曲挠度的解析解；根据位移边界条件，得到了位移系数；根据曲梁内力方程，建立了以矩阵形式表达的刚度平衡方程；经矩阵变换得到了曲梁弯扭分析的刚度矩阵模型以及等效节点力向量。本模型基于梁的刚度平衡方程，采用了精确的解析解，以矩阵形式表达了梁节点位移与节点力之间的关系，利用该模型，可对拱形温室的纵向抗风性能进行分析。

Abstract:

In order to study the roof arch structure in the longitudinal wind resistance analysis of arched greenhouse, based on the geometric equations, equilibrium equations and physics equations of curved beam, its torsion angle and bending deflection control equation considering bending-torsion coupling was developed, and the analytical solutions of torsion angle and bending deflection expressed by primary function vector and integration constant were derived. Then the displacement coefficient was obtained according to displacement boundary condition, and the stiffness equilibrium equation in matrix was established in line with equations of internal forces. After matrix transformation, stiffness matrix model and equivalent nodal force vector for the bending-torsion coupling analysis of curved beam were achieved. It is a model based on the stiffness equilibrium equation and used the accurate analytical solution, the nodal displacement and nodal force were expressed in matrix according to this model. By using this model, the longitudinal wind resistant performance of arch greenhouse can be analyzed.