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

Ahmad R. Najafi, Masoud Safdari, Daniel A. Tortorelli, Philippe H. Geubelle

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)927-954
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Issue number10
StatePublished - Sep 7 2017


  • GFEM
  • analytical sensitivity analysis
  • fixed grid
  • gradient-based shape optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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