On accuracy problems for semi-analytical sensitivity analyses

The semi-analytical method of sensitivity analysis combines ease of implementation with computational efficiency. A major drawback to this method, however, is that severe accuracy problems have recently been reported. A complete error analysis for a beam problem with changing length is carried out in this paper. It is shown that the sensitivity error is proportional to the relative length difference, but in agreement with Eq. 3.8. The approximate pseudo loads thus violate moment equilibrium for rigid body motion while the correct pseudo loads do not.

It might be a good idea to modify the approximate pseudo loads in order to obtain general load equilibrium with rigid body motions. Such a method would be readily applicable for any element type, whether analytical expressions for the element stiffnesses are available or not. This topic is postponed for a future study.