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Shape sensitivity analysis in the extended finite element method
Author(s) -
Barthold FranzJoseph,
Materna Daniel
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210335
Subject(s) - classification of discontinuities , finite element method , sensitivity (control systems) , extended finite element method , context (archaeology) , displacement (psychology) , computer science , mathematics , mixed finite element method , work (physics) , algorithm , mathematical analysis , mathematical optimization , structural engineering , engineering , mechanical engineering , geology , psychology , paleontology , electronic engineering , psychotherapist
The contribution is concerned with the derivation and implementation of shape sensitivity analysis in the context of the extended finite element method (xfem). Here, the displacement approximation is enhanced in order to model strong and weak discontinuities along the interfaces and cracks. Consequently, sensitivity analysis must be accomplished for the extended formulation based on a sub‐integration technique on sub‐domains of the cut elements. This cumbersome and error‐prone work can be circumvent using a standard treatment of sub‐elements on an appropriately defined sub‐mesh. These modifications guarantee exact analytical sensitivities even for distorted finite element domains. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)