SPP 1886 - Polymorphic Uncertainly Modelling for the Numerical Design of Structures
Type of Funding: DFG Programmes, Priority Programmes
Abstract:
The consideration of different uncertainties is a fundamental problem in the optimization of tailor-made, crash-relevant car parts, as well as in their numerical structural analysis itself. These uncertainties are associated with material properties which are dominated by uncertainties on smaller scales, with the production process and with load scenarios which must be expected during the lifetime of the components. Especially due to adaptation strategies such as the concept of "tailored blanks" or local laser hardening, essential material properties for crash safety vary over time due to cyclic loading under normal conditions of use. This leads to comparatively large additional uncertainties for the analysis of the crash scenario. Therefore, the main goal of this proposal is the development of methods for the reliability-based design optimization of tailored, crash-relevant car parts under polymorphic uncertainty. The central issue is the maximization of target values while at the same time setting upper limits for the probability of failure. The methods are based on a Dirac-measure discretization of the epistemic fuzziness and therefore no assumptions regarding the kind of distribution functions of these fuzziness are necessary. The aleatory uncertainties are included by means of a nested, improved Monte Carlo analysis in combination with a suitable substitute model. The Dirac measure discretization is extended with respect to the following aspects: (i) combination with fuzzy variables for the description of epistemic design parameters, (ii) embedding in the concept of alpha-level discretizations and (iii) extension for the calculation of optimal limits of propagated uncertainties of optimization targets. For the calculation of the target variables as well as the mechanical failure variables, a realistic computer model for the simulation of crash loads is constructed, which includes the relevant production processes, such as the forming process for mapping the residual stresses. Furthermore, a new method is being developed for the consideration of local variations of material properties by means of special substitute models based on neural networks and random field realizations. These are configured by data-based identification of real property fields and construction of artificial random field realizations that follow real local distributions and correlations. By including a double nested Monte-Carlo algorithm, the fuzziness of the computer model used for training the neural network is controlled. The developed methods are examined within the framework of realistic optimization problems of crash-loaded car parts as well as on the basis of benchmark problems defined in SPP 1886.
Contact Person at UA Ruhr:
Prof. Dr.-Ing. Daniel Balzani, Ruhr-Universität Bochum