Comparison of different sensitivity matrices relating element elongations to structural response of pin-jointed structures

The sensitivity matrix relating the element elongations to the structural responses is widely used in structural control and error sensitivity analysis of pin-jointed structures. Different sensitivity matrices derived by using different methods have been utilized in previous studies while the relationship between them is still not clear. In this paper, it is theoretically proved that these sensitivity matrices are not equivalent; the essential difference between them is whether the geometrical stiffness is considered. Typical numerical examples are carried out to compare the impacts of different sensitivity matrices on the computation of structural responses (i.e., element forces and nodal displacements). The results show that the computation by using the sensitivity matrix considering the geometrical stiffness is much more accurate. The results also indicate that using the less accurate sensitivity matrices can satisfy the engineering requirements in given applications, but it may cause unacceptable errors in some specific cases. This study gives a rigorous comparison of the existing sensitivity matrices of pin jointed structures with theoretical proof and numerical demonstration, the results of which can provide a useful reference on the future application of the sensitivity matrices.