Sensitivity Analysis

When solving nested structural optimization problems by generating a sequence of explicit first order approximations, such as MMA, one needs to differentiate the objective function and all constraint functions with respect to the design variables. The procedure to obtain these derivatives, or sensitivities, is called sensitivity analysis. In the previous chapter we determined the sensitivity of the compliance of a truss with respect to the cross-sectional area of the bars. In this chapter we will go further and describe how to perform a sensitivity analysis for arbitrary functions and design variables. There are two main groups of methods: numerical methods, which are all approximate, and analytical methods, which are exact. One may also consider hybrids of methods from these two groups: so-called semianalytical methods.