A gradient-based shape optimization scheme using an interface-enriched generalized FEM

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

Research output: Contribution to journalArticlepeer-review


A gradient-based shape optimization scheme using an Interface-enriched Generalized Finite Element Method (IGFEM) is presented wherein the design geometry is projected onto a fixed mesh and the IGFEM is used for analysis. This approach eliminates the mesh distortion present in conventional Lagrangian shape optimization methods, as well as the need for remeshing. An analytical sensitivity analysis using both the adjoint or direct approaches is presented to compute derivatives of the objective and constraint functions. Due to the fixed nature of the mesh, the so-called design velocity field only needs to be computed on the structure boundary/interface. A comparison between IGFEM- and conventional FEM-based shape optimization schemes is presented, showing an improved precision for the IGFEM approach. Finally, we solve various numerical examples to demonstrate the capability of the method including the computational design of particulate and microvascular composites.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Nov 1 2015


  • Analytical sensitivity analysis
  • Fixed grid
  • GFEM
  • Gradient-based shape optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


Dive into the research topics of 'A gradient-based shape optimization scheme using an interface-enriched generalized FEM'. Together they form a unique fingerprint.

Cite this