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Simultaneous shape and topology optimization on unstructured grids

Dahlberg, Vilmer LU ; Dalklint, Anna LU and Wallin, Mathias LU (2025) In Computer Methods in Applied Mechanics and Engineering 438.
Abstract

In this work we present a simultaneous shape and topology optimization framework that generates large-scale 3D designs on unstructured grids. We consider a “parameter-free” shape optimization approach, wherein the nodal coordinates in the finite element mesh serve as design variables. To regularize the design changes we use a PDE-based filter, similar to the filtering techniques used in topology optimization. We present a variant of the “parameter-free” shape optimization where we allow not only design variables on the surface, but also in the bulk of the domain. To combat mesh quality issues we employ adaptive mesh refinement based on a Riemannian metric. The numerical algorithm is implemented in C++ and uses PETSc for efficient shape... (More)

In this work we present a simultaneous shape and topology optimization framework that generates large-scale 3D designs on unstructured grids. We consider a “parameter-free” shape optimization approach, wherein the nodal coordinates in the finite element mesh serve as design variables. To regularize the design changes we use a PDE-based filter, similar to the filtering techniques used in topology optimization. We present a variant of the “parameter-free” shape optimization where we allow not only design variables on the surface, but also in the bulk of the domain. To combat mesh quality issues we employ adaptive mesh refinement based on a Riemannian metric. The numerical algorithm is implemented in C++ and uses PETSc for efficient shape and topology optimization of complex 3D geometries on unstructured grids. We verify our “parameter-free” shape optimization on two examples, and compare different variations of the shape filter. Finally, we demonstrate the power and flexibility of our simultaneous shape and topology optimization framework on a dam-like geometry.

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type
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publication status
published
subject
keywords
Fictitious energy, PETSc, Shape optimization, Topology optimization
in
Computer Methods in Applied Mechanics and Engineering
volume
438
article number
117830
publisher
Elsevier
external identifiers
  • scopus:85217888664
ISSN
0045-7825
DOI
10.1016/j.cma.2025.117830
language
English
LU publication?
yes
id
016caa35-b028-4402-92d5-5b625c1fad46
date added to LUP
2025-06-10 10:36:55
date last changed
2025-06-10 10:38:09
@article{016caa35-b028-4402-92d5-5b625c1fad46,
  abstract     = {{<p>In this work we present a simultaneous shape and topology optimization framework that generates large-scale 3D designs on unstructured grids. We consider a “parameter-free” shape optimization approach, wherein the nodal coordinates in the finite element mesh serve as design variables. To regularize the design changes we use a PDE-based filter, similar to the filtering techniques used in topology optimization. We present a variant of the “parameter-free” shape optimization where we allow not only design variables on the surface, but also in the bulk of the domain. To combat mesh quality issues we employ adaptive mesh refinement based on a Riemannian metric. The numerical algorithm is implemented in C++ and uses PETSc for efficient shape and topology optimization of complex 3D geometries on unstructured grids. We verify our “parameter-free” shape optimization on two examples, and compare different variations of the shape filter. Finally, we demonstrate the power and flexibility of our simultaneous shape and topology optimization framework on a dam-like geometry.</p>}},
  author       = {{Dahlberg, Vilmer and Dalklint, Anna and Wallin, Mathias}},
  issn         = {{0045-7825}},
  keywords     = {{Fictitious energy; PETSc; Shape optimization; Topology optimization}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Computer Methods in Applied Mechanics and Engineering}},
  title        = {{Simultaneous shape and topology optimization on unstructured grids}},
  url          = {{http://dx.doi.org/10.1016/j.cma.2025.117830}},
  doi          = {{10.1016/j.cma.2025.117830}},
  volume       = {{438}},
  year         = {{2025}},
}