Instability Load Analysis For Large-Scale Boom Structures Of Cranes

Large-scale boom structures of cranes are kind of slender flexible heavy-load structures. Due to the advantages of large lifting capacity, high lifting height, wide lifting radius and diverse combination of boom sections, large-scale boom structures are widely used in the fields of hoisting equipments and are the main load-carrying components in the hoisting process. The length of the large-scale boom structures can usually reach dozens or even hundreds of meters to fulfill the high lifting tasks. After carrying heavy loads, large-scale boom structures often show strong geometrical nonlinear behaviors, which makes the equilibrium path following and the instability loads identifying analysis difficult. With the development of modern computing technology and higher requirements in engineering practices, these structures are progressively optimized towards light, sparse and slender. In general, the more slender such structures become, the more likely they lose stability before damage. Furthermore, many factors need to be considered in the lifting performance analysis of large-scale boom structures of cranes, such as:mechanism displacement constraints, multiple loading conditions, and the gravity of boom structures. Therefore, an efficient method for identifying the instability loads of this kind of structures is urgently needed. In order to efficiently solve the critical loads for large-scale boom structures of cranes, this paper studies and discusses the efficient modeling methods and the fast identifying methods for instability loads.Many large-scale industrial equipments or building structures are composed of many standard components. We put forward an overall analysis scheme for these large-scale structures, and presented a new seaming method to assemble these components without recourse to the interface element. Taking the finite element models of components in the design phase as substructures, and then assembling these substructures for the whole analysis by directly giving the relationship between boundary nodal displacements on their common interface, can significantly improve the modeling efficiency. Large-scale boom structures are composed of a series of boom sections, and many of them are periodical. By using the presented method, once the periodic boom section elements have formulated, they can be used repeatedly for the overall modeling of many large-scale boom structures, which can significantly reduce the modeling time. The presented method can also be used for other large-scale sturctures, and the application of the substructure method is further extended.The gravity of large-scale boom structures has a great influence on their stability analysis. Including the discretization of gravity, a static condensation procedure for the boom section element is formulated. By introducing a gravity influence coefficient matrix, the gravity is discreted to each node in the boom structure. Taking each boom section as a unit, the large-scale boom structure can be divided into several boom section elements on which a local coordinate system is defined. The interface nodes of the generated boom section element are defined as its boundary nodes. In addition to gravity, there is no other external force on the boom section internal nodes. Therefore, the displacements of the internal nodes can be represented by the combination of local displacements of boundary nodes and the global displacements of the local coordinate system. Then the gravity work can be divided into two parts:the gravity work related to local displacement, and the gravity work related to global displacements of the local coordinate system. Then the local displacements of internal nodes can be represented by the local displacements of boundary nodes, and finally a new boom section element is formulated for the geometrical nonlinear instability analysis of large-scale boom structures, including the static condensation procedure of gravity. After that, the relationship between the boundary node displacements and boundary nodal forces is derived, and the expression of generalized nodal force of the boom section element is obtained by the boundary node displacement parameters. As accurate structural tangent stiffness matrices are essential to stability analysis, the method to systematically obtain them is discussed by taking the derivative of the generalized nodal forces with respect to the global structural displacements.In this paper, the co-rotational formulation is adopted to describe the geometrical nonlinear behaviors of the boom structures. The luffing mechanism and the boom structure are taken as a whole system for the stability analysis of cranes in engineering practice, and the tensile forces of luffing cables related to the guyed mast rotation or the luffing rope reeved between pulleys are deduced. In practical engineering, the geometrical nonlinear instability analysis of the same type crane requires to fulfill under a series of loading conditions. The traditional incremental methods and various arc-length methods are hard to meet the requirements of high solving speed and efficiency. Considering the lifting load is the only changing load on the crane, the rate form of equilibrium equations can be obtained by taking the derivatives of the load-control parameter. Consequently, the traditional methods for path following will be transformed into the solution of the differential equations. After that, the instability loads of slender large-scale boom structures can be identified by monitoring the rapid changes in the derivatives of displacements and the singularity of the tangent stiffness matrix. Based on the proposed methods in this paper, we build instability loads analysis software for large-scale boom structures of cranes. Using this software, the instability loads of a variety of large-scale boom structures with auxiliary bracings in the practical engineering are identified. The results indicate that, the presented method can efficiently identify critical loads of large-scale slender boom structures, and can be used as a valuable reference for the lifting capacity analysis of these boom structures.