Model reduction in stochastic structural dynamics

Realistic modeling of structures depends on both refined finite element models and the incorporation of uncertainties inherent to geometric, structural and loading parameters. The resulting computational cost, which is necessary to carry out the reliability assessment due to dynamic loading, is generally very high. Several methods are applicable for performing an efficient stochastic dynamic reliability analysis, such as model reduction techniques, response approximation or parallel computation. In the case of dynamically loaded structures, the safety assessment if of high practical relevance due to associated disastrous damages in terms of economical losses and harm of people in the case of structural failure. In structural dynamics, failure can be described as an event occurring in the range of two main mechanisms, namely first exceedance failure and failure due to damage accumulation. The proposed project will deal with the establishment of highly accurate reference solutions of the response distribution of hysteretic oscillators and the enhancement of a method developed at the beginning of the doctoral studies for highly non-linear oscillators. This research area is of enormous interest for the research community, because only for very restricted cases of the loading process, an analytical solution for the first excursion and the crossing rate of the structural response process can be obtained. The main part of the proposed research project deals with the use of model reduction and response approximation schemes for finite element models. The scope of applying meta-models is to provide a simple relation between the input data and output quantities of interest at low computational cost. The mode-based meta-model, which has been introduced by the applicant, will allow for substantial reduction of the computational costs associated with the stochastic structural dynamics analysis. The planned investigations will provide efficient tools for the reliability assessment and structural optimization of structures with uncertainties subjected to dynamic loading. Over all, this research project provides the opportunity for the applicant to collaborate with Professor L.A. Bergman, head of the Department of Aerospace engineering of the University of Illinois at Urbana-Champaign. This collaboration will offer the possibility to work at a research institute with international standards of excellence, which will positively affect a successful elaboration of the innovative contributions discussed in this proposal. The proposed work of the applicant perfectly integrates with the research carried out by the group of the host institute, either for non-linear oscillators subjected to stochastic excitation as well as for model reduction in context with finite element assessment for dynamically loaded structures.