Sophisticated computational techniques for damage mechanics with mixed uncertain input fields
Goal of this research project is to provide efficient computational techniques for detailed damage mechanics finite element models with uncertain input variables. For the treatment of epistemic uncertainties, i.e. unknown input random field parameters, a Dempster-Shafer p-box approach will be utilized and implemented into an adaptive nested sampling strategy. Systematic studies on the discretization of p-boxes in dependency on the input field modeling approach, alternatively via Karhunen-Loeve expansion (KLE) or Polynomial Chaos expansion (PCE) will be investigated. An adaptive multi-level Monte-Carlo scheme will be applied for an efficient sampling of the structural response surfaces. This scheme has to be extended for the nested epistemic-aleatory sampling defining some sophisticated error criteria.
With emphasis to sensitivity or reliability analysis response surfaces for the quantities of interest, i.e. remaining load bearing capacity, will be generated. Here an adaptive generalized Polynomial Chaos (gPC) scheme will be implemented, where for the epistemic parameter space newer developments on elementwise gPC appears an attractive option. Systematic studies on the efficient and accurate construction of possibly element-wise orthogonal polynomials have to be performed. The applicability of the developed computational approach will be studied on our own 3-dimensional bench-mark problem on a concrete beam subjected to 4 point bending loads. This example serves for parametric studies of the overall computational approach.
M.Sc. Mona Dannert
M.Sc. Mona Dannert
Institut für Baumechanik und Numerische Mechanik
Leibniz Universität Hannover
Dr. Rodolfo Miguel Nogueira Fleury
Dr. Rodolfo Miguel Nogueira Fleury Institut für Baumechanik und Numerische Mechanik Leibniz Universität Hannover
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M.M. Dannert, R.M.N. Fleury, A. Fau, U. Nackenhorst (2019),
Non-linear Finite Element Analysis under Mixed Epistemic and Aleatory Uncertain Random Field Input. In: M. Beer and E. Zio (Eds.) Proceedings of the 29th European Safety and Reliability Conference (ESREL), Hannover, Germany - M.M. Dannert, A. Fau, R.M.N. Fleury, M. Broggi, U. Nackenhorst, M. Beer (2019), A collocation scheme for deep uncertainty treatment. 13th International Conference on Application of Statistics and Probability in Civil Engineering (ICASP13), Seoul, South Korea
- F.N. Schietzold, A. Schmidt, M.M. Dannert, A. Fau, R.M.N. Fleury, W.Graf, M. Kaliske, C. Könke, T. Lahmer, U. Nackenhorst (2019),
Developement of fuzzy probability based random fields for the numerical strucutral design, GAMM-Mitteilungen (42:e201900004) - M.M. Dannert, A. Fau, R.M.N. Fleury, M. Broggi, U. Nackenhorst, M. Beer (2018),
A probability-box approach on uncertain correlation lengths by stochastic finite element method. Proc. Appl. Math. Mech. - M.M. Dannert, A. Fau, M. Broggi, U. Nackenhorst, M. Beer (2017),
A nested collocation algorithm for mixed aleatory and epistemic uncertainties using a probability-box approach, in: C. Bucher, B.R. Ellingwood, D.M. Frangopol (Eds.), Safety, Reliability, Risk, Resilience and Sustainability of Structures and Infrastructure, Proceedings of the 12th International Conference on Structural Safety and Reliability (ICOSSAR), Vienna, 820-829