A fuzzy finite element method for sparse experimental data based on a possibilistic approach. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Dridger, Alex; Caylak, Ismail; Mahnken, Rolf
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 55
• Page End: 56
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710016
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: This work considers the possibilistic interpretation of the fuzzy set theory for the fuzzy finite element method (FFEM). The underlying uncertainty type of design variables arises from sparse experimental data and is referred to as imprecise probability. In this context, a linear elastic body with given sparse experimental results for the design variables Young's modulus and Poisson's ratio is studied. To this end, the fuzzy input parameters are represented by possibility distributions generated by a probability‐possibility transformation. A computational approach involving the α‐level discretization technique [4] is applied in order to calculate the possibility of a quantity of interest. Finally, our method is applied in a numerical example for a plate with a ring hole. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)