伸缩臂结构超级单元建模及失稳荷载快速搜索方法

Super element modeling and critical load′s rapid searching method for telescopic boom structures

流动式起重机伸缩臂是典型的嵌套式细长结构,传统等效阶梯梁模型无法正确反映臂节间的约束关系;常用的壳单元模型需建立大量的单元和接触对,影响计算效率和收敛性.结合伸缩臂结构的特点,选择反映截面形状的特征点作为节点,沿臂节纵向划分若干梁单元.以相邻臂节间接触截面节点作为边界点划分子结构,建立随子结构运动的随动坐标系,通过内部自由度凝聚至边界点,获得几何非线性超级单元.考虑内外层臂节间更符合实际机械设备的嵌套式约束关系以及常见的边界条件,给出相应的力学约束模型.得到含荷载参数的结构非线性平衡方程以及相应的切线刚度阵,采用非线性平衡方程的微分形式得到伸缩臂结构的变形平衡路径和失稳荷载.流动式起重机伸缩臂结构数值算例分析表明了方法的有效性及准确性.

The telescopic boom structures of mobile cranes are typical nested slender structures,in which the constraint relationships between boom segments cannot be effectively reflected by the traditional equivalent stepped beam model.While it is necessary to establish lots of elements and contact pairs using general shell elements,which would affect the efficiency and convergence seriously.Firstly,combining the features of telescopic boom structure,feature points adapted to section shape are selected as nodes and each boom segment is divided into several beam elements along the longitudinal direction.Second,the substructures are delimited by taking contact cross-sectional nodes of adjacent boom segments as the boundary points,and an embedded coordinate system is defined.The geometric nonlinear super element is obtained through the condensation of internal degrees of freedom to boundary points.Then the mechanical constraint model is established in accordance with the nested constraint relationships suitable for actual mechanical equipment between inner and outer boom segments and common boundary conditions.And structural nonlinear equilibrium equations with load parameters and corresponding tangent stiffness matrices are derived.Finally,the deformation equilibrium path and critical loads of telescopic boom structures could be obtained by virtue of the differential form of nonlinear equilibrium equations.A numerical example of mobile crane telescopic boom structure is analyzed,which validates the efficiency and accuracy of the proposed method.