基于混合有限元法的钢箱拱相关稳定分析

Interactive stability analysis of steel box arch based on mixed finite element method

针对薄壁结构提出了一种混合有限元方法,对结构关心的部位采用板壳单元模拟,其他部位采用杆系单元模拟,根据平截面假定推导了2种单元在交界面处的约束方程,由此建立整体混合有限元模型。通过算例验证了该方法的可靠性,可以计算薄壁结构的整体稳定、局部稳定和整体局部相关稳定。用该方法对某座刚构-单肋钢箱系杆拱组合桥梁进行特征值和弹塑性稳定分析,得到了相应的稳定系数和失稳模态。实例显示,该方法既可以弥补梁单元模型无法计算构件局部屈曲的不足,又可克服局部板壳模型无法准确模拟其整体边界条件及工作环境的缺点,还可以避免全结构板壳模型产生过多单元数量和庞大结构刚度矩阵的弊端,计算可靠性和计算效率大大提高。

A mixed finite element method was used to analyze thin-walled structures,in which the concerned parts were modeled by plane or shell elements,and the unconcerned parts were modeled by beam or link elements.The constraint equations were established at the common boundary section based on plane section premise.Consequently, the whole mixed finite element model was established by this theory.The method can be used to calculate thin-walled structures not only overall stability but also local stability and interactive stability.A combinational bridge with rigid frame and single-ribbed steel box arch was computed by this method for eigenvalue stability and elastoplastic stability,and the stability coefficients and buckling modes were obtained.All examples show that this method can not only make up for deficiency of local buckling analysis of beam element model of the components,but also overcome the drawback of inaccurate simulation of the overall boundary conditions and working environment in partial shell model.Turthermore,the shortcoming of too many elements and huge structural stiffness matrix in whole shell model can be avoided.Therefore,calculating reliability and efficiency are greatly enhanced.