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Shape optimization using a NURBS‐based interface‐enriched generalized FEM
Author(s) -
Najafi Ahmad R.,
Safdari Masoud,
Tortorelli Daniel A.,
Geubelle Philippe H.
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5482
Subject(s) - finite element method , sensitivity (control systems) , shape optimization , interface (matter) , mathematics , mathematical optimization , constraint (computer aided design) , b spline , algorithm , computer science , geometry , mathematical analysis , structural engineering , engineering , bubble , maximum bubble pressure method , parallel computing , electronic engineering
Summary This study presents a gradient‐based shape optimization over a fixed mesh using a non‐uniform rational B‐splines‐based interface‐enriched generalized finite element method, applicable to multi‐material structures. In the proposed method, non‐uniform rational B‐splines are used to parameterize the design geometry precisely and compactly by a small number of design variables. An analytical shape sensitivity analysis is developed to compute derivatives of the objective and constraint functions with respect to the design variables. Subtle but important new terms involve the sensitivity of shape functions and their spatial derivatives. Verification and illustrative problems are solved to demonstrate the precision and capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.