Flexibility Method - Advantages and Disadvantages

Advantages and Disadvantages

While the choice of redundants in (4) appears to be arbitrary and troublesome for automatic computation, this objection can be overcome by proceeding from (3) directly to (5) using a modified Gauss-Jordan elimination process. This is a robust procedure that automatically selects a good set of redundant forces to ensure numerical stability.

It is apparent from the above process that the matrix stiffness method is easier to comprehend and to implement for automatic computation. It is also easier to extend for advanced applications such as non-linear analysis, stability, vibrations, etc. For these reasons, the matrix stiffness method is the method of choice for use in general purpose structural analysis software packages. On the other hand, for linear systems with low degree of statical indeterminacy, the flexibility method has the advantage of being computationally less intensive. This advantage, however, is a moot point as personal computers are widely available and more powerful. The main redeeming factor in learning this method nowadays is its educational value in imparting the concepts of equilibrium and compatibility in addition to its historical value. In contrast, the procedure of the direct stiffness method is so mechanical that it risks being used without much understanding of the structural behaviors.

The upper arguments were valid up to the late 1990s. However, recent advances in numerical computing have shown a come back of the force method, especially in the case of nonlinear systems. New frameworks have been developed that allow "exact" formulations irrespectively of the type or nature of the system nonlinearities. The main advantages of the flexibility method is that the result error is independent of the discretization of the model and that it is indeed a very fast method. For instance, the elastic-plastic solution of a continuous beam using the force method requires only 4 beam elements whereas a commercial "stiffness based" FEM code requires 500 elements in order to give results with the same accuracy. To conclude, one can say that in the case where the solution of the problem requires recursive evaluations of the force field like in the case of structural optimization or system identification, the efficiency of the flexibility method is indisputable.