WIAS Preprint No. 2629, (2019)

Topology optimization subject to additive manufacturing constraints


  • Ebeling-Rump, Moritz
  • Hömberg, Dietmar
  • Lasarzik, Robert
    ORCID: 0000-0002-1677-6925
  • Petzold, Thomas

2010 Mathematics Subject Classification

  • 49Q10 74P05 49Q20 65M60 74P10


  • Additive manufacturing, topology optimization, linear elasticity, phase field method, optimality conditions, numerical simulations




In Topology Optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg-Landau term. During 3D Printing overhangs lead to instabilities, which have only been tackled unsatisfactorily. The novel idea is to incorporate an Additive Manufacturing Constraint into the phase field method. A rigorous analysis proves the existence of a solution and leads to first order necessary optimality conditions. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the Additive Manufacturing Constraint brings about support structures, which can be fine tuned according to engineering demands. Stability during 3D Printing is assured, which solves a common Additive Manufacturing problem.

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