Design sensitivity analysis: Overview and review

Design sensitivity plays a critical role in inverse and identification studies, as well as numerical optimization, and reliability analysis. Herein, we review the state of design sensitivity analysis as it applies to linear elliptic systems. Both first- and secondorder sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. Although these results are not new, some of the derivations offer a different perspective than those previously presented. This article is meant as a tutorial, and as such, a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses. However, the concepts presented in this trivial example may be readily extended to compute sensitivities for complex systems via numerical techniques such as the finite element, boundary element, and finite difference methods.