Introduction to Variational Sensitivity Analysis

The methods for discrete sensitivity analysis discussed in the previous chapter are very general in that they are equally applicable to nonstructural sensitivity analysis involving systems of linear equations, eigenvalue problems, etc. However, for structural applications they also have two disadvantages. First, not all structural analysis solution methods lead to the type of discretized equations that are discussed in Chapter 7. For example, shell-of-revolution codes such as FASOR [1] directly integrate the equations of equilibrium without first converting them to systems of algebraic equations. Second, operating on the discretized equations often requires access to the source code of the structural analysis program which implements these equations. Unfortunately, many of the popular structural analysis programs do not provide such access to most users. It is desirable, therefore, to have sensitivity analysis methods that are more generally applicable and can be implemented without extensive access to and knowledge of the insides of structural analysis programs. Variational methods of sensitivity analysis achieve this goal by differentiating the equations governing the structure before they are discretized. The resulting sensitivity equations can then be solved with the aid of a structural analysis program. It is not even essential that the same program be used for the analysis and the sensitivity calculations.