Geometrically Nonlinear Stability Analysis Of Slender Structures

Slender structures are widely used in engineering practice, such as a variety of crane booms and aerial platform vehicle, etc. Instability becomes one of the main forms of failures for such structures, so it must be taken into account in the design process. Eigenvalue buckling analysis is the main method of structural stability because of its computational efficiency. However, eigenvalue buckling analysis is based on the linear relationship between stress and load, and obvious deformation occur before buckling for many of slender structure, ignoring geometric nonlinear effects will result a large deviation with actual situation.Based on the existing research results of structural stability, stability of slender structure is studied in this paper with the actual example of crane boom. Using co-rotational approach, corresponding geometric nonlinear equilibrium equation is established, and element tangent stiffness matrix is not required to solve the equation, that simplify the modeling of stability; the Jacobian matrix of equilibrium equation is derived in order to improve the solving efficiency, and this derivation is independent of element forms; the scale of solution is greatly reduced using the method of condensing the internal DOF of sub-structure into boundary.Based on the above theory, finite element software is developed to analyze the geometrically nonlinear stability of slender structure. The bucking analysis of actual crane boom is done using this software, and the results of analysis verify the correctness and effectiveness of the methods in this paper.