Geometrical nonlinear and stability analysis for slender frame structures of crawler cranes

• The first critical load for lattice-boom structures of crawler cranes is determined.
• The methodology is the path-following method based on the governing equations in rate form.
• An element-independent co-rotational substructure element formulation is presented.
• Accurate tangent stiffness matrices and external forces of movable boundaries are formulated.

The geometrical nonlinear and stability analysis for slender frame structures of crawler cranes is investigated in this paper. Taking each lattice-boom section as a super element, the slender frame structures are divided into several substructures and an element-independent co-rotational substructure element is formulated based on the co-rotational method. Owing to the small local nodal displacements and the reinforced end sections of substructures, the degrees of freedom of the internal and boundary nodes can be related to the motions of the two end sections, which results in that each substructure is regarded as a generalized 3D two-node beam element. The generalized internal nodal and gravity forces for super elements as well as the accurate tangential stiffness matrices are formulated. In consideration of movable boundaries of the lattice-boom structures, the additional external nodal forces and their derivatives on the structural and mechanical displacements are given for the residual force equations. After these preparations, a new methodology for determining the first critical load of crawler crane lattice-boom structures is presented, based on solving the governing equations in rate form and combining the instability criterion. At last, a cantilever beam, a space slender frame structure and a certain type of crawler crane with lattice-boom structures are presented respectively, which prove the validity and rationality of the analytical procedure.