Variational sensitivity analysis and changes in the material configuration

This contribution is concerned with some aspects of variational design sensitivity analysis in the physical and material configuration. Sensitivity analysis is a branch of structural optimization, e.g. shape or topology optimization. In these disciplines we consider variations of the material configuration and we are interested in the change of the state variables and the objective functional due to these variations. In the context of structural optimization this is termed as design sensitivity analysis. The sensitivities are required in order to solve the corresponding Lagrangian equation within standard nonlinear programming algorithms. In many engineering applications, the energy functional of the problem is used as the objective functional. In this paper, we consider variations of the energy with respect to the state and the design and we investigate sensitivity relations for the physical and material problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)