Vol. 7, No. 2, 2019

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A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics

Eduard Penner, Ismail Caylak, Alex Dridger and Rolf Mahnken

Vol. 7 (2019), No. 2, 99–129
Abstract

This work is focused on polymorphic uncertainties in the framework of constitutive modeling for transversely isotropic materials. To this end, we propose a hybrid fuzzy-stochastic model, where the stochastic part accounting for aleatory uncertainties of material parameters is expanded with the multivariate polynomial chaos expansion. In order to account for epistemic uncertainties, polynomial chaos coefficients are treated as fuzzy variables. The underlying minimum and maximum optimization problem for the fuzzy analysis is approximated by α-level discretization, resulting in a separation of minimum and maximum problems. To become more universal, so-called quantities of interest are employed, which allow a general formulation for the target problem. Numerical examples with fuzzy, fuzzy-stochastic, and hybrid fuzzy-stochastic input demonstrate the versatility of the proposed formulation.

Keywords
polymorphic uncertainty, fuzzy, stochastic, fuzzy-stochastic, polynomial chaos expansion, fiber reinforced plastics, transversely isotropic materials, imprecise probability, epistemic, aleatory
Mathematical Subject Classification 2010
Primary: 60A86
Milestones
Received: 6 September 2018
Revised: 9 January 2019
Accepted: 1 March 2019
Published: 27 May 2019

Communicated by Paul Steinmann
Authors
Eduard Penner
Faculty of Mechanical Engineering
Paderborn University
Paderborn
Germany
Ismail Caylak
Faculty of Mechanical Engineering
Paderborn University
Paderborn
Germany
Alex Dridger
Faculty of Mechanical Engineering
Paderborn University
Paderborn
Germany
Rolf Mahnken
Faculty of Mechanical Engineering
Paderborn University
Paderborn
Germany