Overhang Penalization in Additive Manufacturing via Phase Field Structural Topology Optimization with Anisotropic Energies

Harald Garcke, Kei Fong Lam*, Robert Nürnberg, Andrea Signori

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)

Abstract

A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during construction) with anisotropic energy functionals. Convex and non-convex examples are provided, with the latter showcasing oscillatory behavior along the object boundary termed the dripping effect in the literature. We provide a rigorous mathematical analysis for the structural topology optimization problem with convex and non-continuously-differentiable anisotropies, deriving the first order necessary optimality condition using subdifferential calculus. Via formally matched asymptotic expansions we connect our approach with previous works in the literature based on a sharp interface shape optimization description. Finally, we present several numerical results to demonstrate the advantages of our proposed approach in penalizing overhang developments.
Original languageEnglish
Article number44
JournalApplied Mathematics and Optimization
Volume87
Issue number3
Early online date13 Mar 2023
DOIs
Publication statusPublished - Jun 2023

Scopus Subject Areas

  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Topology optimization
  • Phase field
  • Anisotropy
  • Linear elasticity
  • Optimal control
  • Additive manufacturing
  • Overhang penalization

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