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

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.