Efficient Inverse-designed Structural Infill for Complex Engineering Structures

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Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for additive manufacturing, infill is often neglected as a component of the optimized structure. In this paper, both concerns are addressed using a so-called de-homogenization topology optimization procedure on complex engineering structures discretized by 3D unstructured hexahedrals.

Using a rectangular-hole microstructure (reminiscent to the stiffness optimal orthogonal rank-3 multi-scale) as a base material for the multi-scale optimization, a coarse-scale optimized geometry can be obtained using homogenization-based topology optimization. Due to the microstructure periodicity, this coarse-scale geometry can be up-sampled to a fine single-scale physical geometry with optimized infill, with only a minor loss in structural performance and at a fraction of the cost of a fine-scale solution.The upsampling on 3D unstructured grids is achieved through stream surface tracing, aligning with the optimized local orientations. The periodicity of the physical geometry can be tuned, such that the material serves as a structural component and also as an efficient infill for additive manufacturing designs.

The method is demonstrated through three examples of varying geometrical complexity. It achieves comparable structural performance to “brute force” state-of-the-art methods but stands out for its significant computational time reduction. By allowing multiple active layers, the mapped solution becomes more mechanically stable, leading to an increased critical buckling load factor without additional computational expense. The control of active layers also provides direct control over the internal structure, i.e., infill, ensuring that the infill is incorporated as a structural component and enhancing the manufacturability of the de-homogenization procedure. Furthermore, the proposed approach exhibits promising results, achieving volume fractions and weighted compliance values within 5% of the large-scale SIMP model, while demonstrating a computational efficiency improvement ranging from 10 times to over 250 times.
Original languageEnglish
Article number111427
JournalThin-Walled Structures
Number of pages20
Publication statusPublished - 2024


  • Topology optimization
  • De-homogenization
  • Multiscale
  • Unstructured structures
  • Frame-fields
  • Stream surfaces


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