Shape optimization using a NURBS‐based interface‐enriched generalized FEM |
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| Authors: | Ahmad R. Najafi Masoud Safdari Daniel A. Tortorelli Philippe H. Geubelle |
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| Affiliation: | 1. Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL, USA;2. Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana‐Champaign, Urbana, IL, USA;3. Department of Aerospace Engineering, University of Illinois, Urbana, IL, USA;4. Center for Design and Optimization, Lawrence Livermore National Laboratory Livermore, Livermore, CA, USA |
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| Abstract: | 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. |
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| Keywords: | gradient‐based shape optimization NURBS GFEM fixed grid analytical sensitivity analysis |
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