Localising the smallest stiffness and its direction of a homogeneous structure by spectral and optimisation approaches

•Novel relation between the modal and the static stiffness of a structure.•Identifiability of smallest structural stiffness based on modal properties.•Alternative method for localising the smallest structural stiffness based on structural compliance maximisation. Structural stiffness plays an important role in engineering design. The analysis of stiffness requires precise experiments and computational models that can be difficult or time–consuming to procure. A novel relation between modal and static stiffness based on modal decomposition is introduced in this study. This relation allows analysing the smallest structural stiffness and its direction. Further, it is shown that the smallest stiffness can be found using an optimisation algorithm that is based on the maximisation of structural compliance. Both approaches are compared on several computational examples leading to similar results in terms of smallest stiffness and its direction. The proposed approaches serve as quantitative/qualitative tools for the analyses of structural stiffness, particularly in structural health monitoring.