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 引用本文: 王刚, 齐朝晖, 汪菁. 含铰接杆系结构几何非线性分析子结构方法[J]. 力学学报, 2014, 46(2): 273-283.
Wang Gang, Qi Zhaohui, Wang Jing. SUBSTRUCTURE METHODS OF GEOMETRIC NONLINEAR ANALYSIS FOR MEMBER STRUCTURES WITH HINGED SUPPORTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(2): 273-283.
 Citation: Wang Gang, Qi Zhaohui, Wang Jing. SUBSTRUCTURE METHODS OF GEOMETRIC NONLINEAR ANALYSIS FOR MEMBER STRUCTURES WITH HINGED SUPPORTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(2): 273-283.

## SUBSTRUCTURE METHODS OF GEOMETRIC NONLINEAR ANALYSIS FOR MEMBER STRUCTURES WITH HINGED SUPPORTS

• 摘要: 将细长杆系结构按长度方向划分为多个子结构，由于在子结构坐标系下的节点位移均是小位移，可以将子结构内部自由度凝聚到边界. 考虑到子结构端面在变形过程中保持为刚性截面，将端面节点自由度进一步凝聚到端面形心点，这样每一个子结构就减缩成形式上只有两个节点的广义梁单元，大大减缩了自由度. 大位移大转动是细长杆系结构产生几何非线性效应的一个重要原因，基于共旋坐标法，建立了随单元一起运动的随动坐标系，推导了子结构单元的节点力平衡方程及其切线刚度阵. 同时，考虑到工程机械中细长杆系结构含有相互铰接的刚体加强块，给出了非独立自由度节点力转换到独立参数下的广义节点力及其导数. 最后，通过履带式起重机的副臂工况算例，给出了其在不同载荷下的臂架结构位移，验证了方法的正确性.

Abstract: Along the longitudinal direction, a slender truss structure is divided into several substructures. Due to that the nodal displacements are small in the embedded coordinate systems of substructures, the degrees of freedom of the internal nodes can be reduced to the ones of the interface nodes. Considering that the left and right ends of the substructure remain rigid sections during deformation, the interface nodal displacements would be reduced to the ones of the section central points. Each substructure would be reduced to be a generalized two-node beam element, in which the degree of freedom would be reduced sharply. Large displacement and rotation are important causes of the geometric nonlinearity of slender member structures. Based on the co-rotational method, an embedded coordinate system is defined, and the equilibrium equations of nodal forces for substructure elements and the tangential stiffness matrix are formulated. Taking into account of slender truss structures containing mutually hinged rigid bodies in the actual construction machinery, the convention of the nodal forces and their derivatives with respect to the independent and non-independent degrees of freedom are formulated. At last, numerical examples of sub-arm condition for crawler cranes are presented, in which the displacements of the boom structures under different load conditions are obtained. The numerical examples prove the validity of the presented method.

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