Error control and adaptive methods for the sensitivity error for large geometry changes based on exact variational formulations

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Structures can nowadays be efficiently designed on the basis of the technological progress and improved production methods. An important role plays the optimization of the geometry of components in order to reduce the weight and to save material resources. Sensitivity analysis is a central part for the solution of optimization problems as well as parameter studies. It yields a prediction for thechange in the structural response due to the change of input parameter (design changes). The accuracy of sensitivity information has an important influence on the convergence speed and efficiency of optimization processes. Almost exclusive first order sensitivity relations are used, which yield for large design changes just a rough approximation for the true change of the structural response. Furthermore,sensitivity analysis is nowadays performed based on numerical solution methods, such as the finite element method. Therefore, two important error sources have to be considered within the sensitivity analysis for large design changes: 1. approximation error (error due to approximation of first order) and 2. discretization error (error due to discretization and solution with numerical methods). The goal is the development of efficient and reliable error estimators for the sensitivity errorfor large geometry changes, which is the combination of both error sources. Furthermore, the sensitivity error is to be minimized by using adaptive methods. The accuracy and reliability of sensitivity information shall be quantified and improved. The improved sensitivity information shall be used in order to increase the efficiency and convergence speed of optimization processes.