TY - JOUR
T1 - A gradient-based shape optimization scheme using an interface-enriched generalized FEM
AU - Najafi, Ahmad R.
AU - Safdari, Masoud
AU - Tortorelli, Daniel A.
AU - Geubelle, Philippe H.
N1 - Funding Information:
This work has been supported by the Air Force Office of Scientific Research Multidisciplinary University Research Initiative under contract # FA9550-09-1-0686 . Support for M. Safdari was provided through a Grant No. FA9550-12-1-0445 to the Center of Excellence on Integrated Materials Modeling (CEIMM) at Johns Hopkins University (partners JHU, UIUC, and UCSB) awarded by the AFOSR/RSL (Computational Mathematics Program, Manager Dr. F. Fahroo) and AFRL/RX (Monitors Dr. C. Woodward and T. Breitzman).
Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - 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.
AB - 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.
KW - Analytical sensitivity analysis
KW - Fixed grid
KW - GFEM
KW - Gradient-based shape optimization
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U2 - 10.1016/j.cma.2015.07.024
DO - 10.1016/j.cma.2015.07.024
M3 - Article
AN - SCOPUS:84939486246
VL - 296
SP - 1
EP - 17
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0374-2830
ER -