The fundamental difference between flexibility and stiffness matrix methods for the analysis of statically indterminate structure, is that
1
The flexibility method chooses the redundant reactions or internal forces while stiffness method consider the nodal displacements as basic unkowns.
2
The number of simultaneous equations to be solved in the flexibility method will be very much smaller than the number of equations involved in the stiffness mathod.
3
In the flexibility matrix, the equations of equilibrium will inevitably be unsymmetric and less sparsely populated while the stiffness matrix is always symmetric and sparsely populated.
4
Flexibility matrix method is suitable to structures with a smaller degree of statical indeterminacy than kinematic indeterminacy while the stiffness matrix method is better suited to structures with a smaller degree at statical indeterminacy than kinematic indeterminacy.