WIAS Preprint No. 2615, (2019)

Structural multiscale topology optimization with stress constraint for additive manufacturing


  • Auricchio, Ferdinando
  • Bonetti, Elena
  • Carraturo, Massimo
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Reali, Alessandro
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X

2010 Mathematics Subject Classification

  • 74P05 49M05 74B99


  • Additive manufacturing, first-order necessary optimality conditions, phase-field method, structural topology optimization, functionally graded material




In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions are rigorously derived and a numerical algorithm which implements the method is presented. A sensitivity study with respect to some parameters is conducted for a two-dimensional cantilever beam problem. Finally, a possible workflow to obtain a 3D-printed object from the numerical solutions is described and the final structure is printed using a fused deposition modeling (FDM) 3D printer.

Appeared in

  • Math. Models Methods Appl. Sci., 30 (2020), pp. 1461--1483, DOI 10.1142/S0218202520500281 with the new title ``A phase-field-based graded-material topology optimization with stress constraint''.

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