An efficient fuzzy non-deterministic approach for structural finite element analysis (Efficiënte vaagheidsgevoelige methode voor structurele eindige-elementen analyse)

Virtual prototyping is a standard tool for the design of mechanical products in a range of engineering application fields. Different virtual prototyping techniques based on numerical simulations enable performance evaluations in early design phases without building physical prototypes. Numerical simulation techniques allow fast and cheap design response prediction, which explains their high value as design evaluation and optimisation tool.In any engineering product or process, non-determinism is present. In numerical simulation techniques the physical non-determinism can be classified into variability and uncertainty. Variability refers to an inherent non-deterministic effect that can be statistically described. A characteristic example of a variability is a specific production process that affects the thickness of a stamped sheet-metal component. Uncertainty is usually due to lack of knowledge at a certain stage of the design that can be reduced as knowledge becomes available. The physical trustworthiness of the computer simulations can be increased by considering the non-determinism on the input physical parameters and by propagating their effect to the numerical results. During the past decades the non-deterministic modelling concepts and methods have increasingly been addressed in research. Although substantial efforts have been invested, non-deterministic modelling tools have not yet become standard in industry, mainly due to the high additional computational burden.This dissertation deals with the development and validation of different approaches for structural uncertainty modelling with the fuzzy finite element method. The main objective of the novel developments is to address the computational efficiency of the interval and fuzzy structural finite element analysis. As first contribution, a reduced optimisation method is proposed in combination with response surface modelling in the context of black-box treatment of the interval and fuzzy problems. The main idea is to apply a parameter reduction strategy in combination with optimisation and response surface modelling in order to reduce complexity of the underlying problem so that the associated computational cost is reduced. The second proposed contribution comprises an efficient reformulation of the classical deterministic finite element process, resulting in the so-called reanalysis-based finite element method. This new approach will allow to efficiently perform iterations of modified finite elements systems, thanks to two key elements, each of which addresses one fundamental step in the finite element solution process. On the one hand, the efficiency of the modified system generation is improved by the introduction of a new fast system regeneration process. On the other hand, the efficiency of the system solution is improved by the application of a tailored reanalysis solver. The proposed methods are validated in terms of accuracy and efficiency on industrial-sized case studies.nrpages: 182status: publishe