{
  "abstract": "Gray elements and material overlaps at the interfaces limit density-based multi-material topology optimization. This article extends the level set-based negative-mapping interpolation to the multi-material proportional topology optimization of macro-scale structures in two and three dimensions. An alternating active-phase algorithm decomposes M-phase problems into two-phase sub-problems described by level set functions; an evolutionary strategy removes the need for sentitivity analysis; and the negative-mapping interpolation eliminates the overlaps of the phases in the interface elements. Cantilever and half-MBB beams in two dimensions and a cantilever beam in three dimensions, with three and four material phases, give smooth boundaries, no gray elements and overlap-free designs. The compliance lies below the SIMP value in four of the eight two-dimensional cases and 0.3%, 0.4%, 4.8% and 12.7% above it in the other four. The influence of the material properties, of the interface treatment and of the algorithmic parameters is also examined.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17963",
  "author_total": 6,
  "authors": [
    {
      "name": "Dong Wang"
    },
    {
      "name": "Qianglin Ran"
    },
    {
      "name": "Xuanliang Wang"
    },
    {
      "name": "Wei Xiang"
    },
    {
      "name": "Wenming Cheng"
    },
    {
      "name": "Run Du"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crk4t7mgwh9f5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17963",
  "fulltext_url": null,
  "id": "crk4t7mgwh9f5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17963",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.17963",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crk4t7mgwh9f5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2608.17963",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17963"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Overlap-free multi-material topology optimization for minimum compliance in two and three dimensions by level-set-based negative-mapping interpolation",
  "title_text": "Overlap-free multi-material topology optimization for minimum compliance in two and three dimensions by level-set-based negative-mapping interpolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/crk4t7mgwh9f5",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1080/0305215x.2026.2746638",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}