Define flexibility and stiffness

Flexibility

Flexibility is the displacement produced by a unit force. The flexibility coefficient $f_{ij}$ is the displacement at coordinate $i$ due to a unit force at coordinate $j$ (all other coordinates free of load). It is a measure of how easily a structure deforms. The flexibility matrix $[F]$ gives $\{\Delta\} = [F]\{P\}$. Its unit is m/kN (or rad/kNm). Example: for a cantilever of length $L$ with a tip load, $f_{11} = \dfrac{L^3}{3EI}$.

Stiffness

Stiffness is the force required to produce a unit displacement. The stiffness coefficient $k_{ij}$ is the force needed at coordinate $i$ to produce a unit displacement at coordinate $j$ while all other coordinates are held fixed. The stiffness matrix $[K]$ gives $\{P\} = [K]\{\Delta\}$. Its unit is kN/m (or kNm/rad). Example: for a beam of length $L$ fixed at both ends, a force of $\dfrac{12EI}{L^3}$ is needed to move one end through a unit deflection while both ends are prevented from rotating. The two matrices are inverses of each other, $[K] = [F]^{-1}$.