Robustness Analysis and Key Element Determination of Framed Structures

A new method is proposed to determine key elements in framed structures, where the relative condition number of the global stiffness matrix is chosen as the quantitative indicator of structural robustness. By comparing the mathematical meaning of the relative condition number with the physical meaning of the structural robustness, the structural robustness can be evaluated from the relative condition number between the modified system and the original structure. A simple statically determinate truss was used to verify the applicability of the proposed approach. A more complex Kiewitt single-layer shell was further adopted to show the effectiveness of the proposed method. The numerical results indicate that the proposed structural robustness indicator can not only clearly reflect the characteristics of framed structures, but also effectively predict the influence of individual structural members on the behaviour of the structural system.