# Solving for stiffness matrix numerically by a set of measurements

Is it in general possible when you have a mechanical structure (in this case I am referring to the structure in this post) and you want to determine the global stiffness matrix of this structure, to solve for the matrix based on measurements?

More specifically, I have a structure where parts are connected by springs. I apply a known force to one of the parts and measure the displacement. In this way I get $$n$$ force/moment - displacement/rotation pairs. Is it possible to solve for a matrix $$K$$, for

$$F = KX$$,

with $$F =\begin{bmatrix}F_x & F_y & F_z & M_x &M_y&M_z\end{bmatrix}$$ and $$X= \begin{bmatrix}dx & dy & dz & \theta_x &\theta_y&\theta_z\end{bmatrix}$$?

Is this feasible from a mechanical point of view, because e.g. this "stiffness matrix" $$K$$ may not be unique according to the load applied? Are there any constraints or requirements regarding the measurements?

P.S. Applied forces are rather small (within the elastic range of the spring) and the displacement is restricted, so no large deflections should occur. This is why I assumed a linear approximation.