Evaluating the stiffness of cable-bar tensile structures based on subspaces of zero elastic stiffness and demand stiffness

Abstract

In-service cable-bar tensile structures inevitably experience various degrees of performance degradation or even structural failure due to factors like member stiffness deterioration. How to quantitatively investigate the effect of member stiffness deterioration on the overall performance of the structure has become a big concern in engineering. To solve this problem, the basic work is to establish the relationship between members’ stiffness and structural stiffness. First, based on the element analysis, the elemental elastic (or geometric) stiffness matrix is uniformly expressed by its stiffness value and direction vector. A new expression of the structural tangent stiffness matrix is then provided, with the grouping of member’s stiffness to structural stiffness clearly illustrated. Second, based on eigen-decompostion of stiffness matrices, the properties of structural elastic stiffness and geometric stiffness are investigated in detail, with the coupling mechanism explained by matrix perturbation theory. The zero elastic stiffness subspace is then suggested, of which the stiffness is mainly constituted by geometric stiffness. Third, the structural demand stiffness, which directly resists the deformations caused by external loads, is extracted from the overall stiffness of the structure. Finally, methods to quantify the stiffness contributions of the structural or elemental stiffness to the zero elastic stiffness subspace or structural demand stiffness subspace are established, by which the key stiffness path of the structure can be found. Two types of cable-bar tensile structures are shown to present the application of the proposed method to real structures. Numerical results show that the proposed method can effectively find the members that contribute the most to resist an external load or stabilize the mechanisms of the structure.