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Title: Shape optimization using a NURBS-based interface-enriched generalized FEM

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. As a result, verification and illustrative problems are solved to demonstrate the precision and capability of the method.

Authors:
 [1];  [2];  [3];  [1]
  1. Univ. of Illinois, Urbana, IL (United States); Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
  2. Univ. of Illinois, Urbana, IL (United States)
  3. Univ. of Illinois, Urbana, IL (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1399734
Report Number(s):
LLNL-JRNL-708998
Journal ID: ISSN 0029-5981
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 111; Journal Issue: 10; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; gradient-based shape optimization; NURBS; GFEM; fixed grid; analytical sensitivity analysis

Citation Formats

Najafi, Ahmad R., Safdari, Masoud, Tortorelli, Daniel A., and Geubelle, Philippe H. Shape optimization using a NURBS-based interface-enriched generalized FEM. United States: N. p., 2016. Web. doi:10.1002/nme.5482.
Najafi, Ahmad R., Safdari, Masoud, Tortorelli, Daniel A., & Geubelle, Philippe H. Shape optimization using a NURBS-based interface-enriched generalized FEM. United States. doi:10.1002/nme.5482.
Najafi, Ahmad R., Safdari, Masoud, Tortorelli, Daniel A., and Geubelle, Philippe H. Sat . "Shape optimization using a NURBS-based interface-enriched generalized FEM". United States. doi:10.1002/nme.5482. https://www.osti.gov/servlets/purl/1399734.
@article{osti_1399734,
title = {Shape optimization using a NURBS-based interface-enriched generalized FEM},
author = {Najafi, Ahmad R. and Safdari, Masoud and Tortorelli, Daniel A. and Geubelle, Philippe H.},
abstractNote = {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. As a result, verification and illustrative problems are solved to demonstrate the precision and capability of the method.},
doi = {10.1002/nme.5482},
journal = {International Journal for Numerical Methods in Engineering},
number = 10,
volume = 111,
place = {United States},
year = {2016},
month = {11}
}

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