Sensitivity of optimum solutions to problem parameters

In an aircraft configuration optimization, the information of interest is the sensitivity of optimal block fuel consumption and wing aspect ratio and area, to variations of required range and payload. The objectives of this study are: (1) to show how the equations capable of yielding the sensitivity derivatives (the sensitivity equations) can be obtained for a constrained optimum regardless of the type of optimization algorithm that was used to arrive at the optimum point, (2) to review the solvability of the sensitivity equations and (3) to report on applications on structural optimization. Numerical examples, which demonstrate the sensitivity analysis, include a tubular column and a three-bar truss for which closed form solutions are obtained, a ten-bar truss that requires the use of a finite element analysis, and a thin-walled beam characterized by strongly nonlinear constraints for local buckling. It is concluded that a practically significant extrapolation accuracy may be obtained for a reasonably broad range of parameter changes; and that accuracy does not depend strongly on the degree of convergence of the optimum solution from which the sensitivity derivatives are obtained.