  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.
