Overlap-free multi-material topology optimization for minimum compliance in two and three dimensions by level-set-based negative-mapping interpolation
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.
Versions
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BibTeX
@misc{wang2026overlapfree,
title = {{Overlap-free multi-material topology optimization for minimum compliance in two and three dimensions by level-set-based negative-mapping interpolation}},
author = {Dong Wang and Qianglin Ran and Xuanliang Wang and Wei Xiang and Wenming Cheng and Run Du},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.17963},
eprint = {2608.17963},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17963},
}
RIS
TY - UNPB
TI - Overlap-free multi-material topology optimization for minimum compliance in two and three dimensions by level-set-based negative-mapping interpolation
AU - Dong Wang
AU - Qianglin Ran
AU - Xuanliang Wang
AU - Wei Xiang
AU - Wenming Cheng
AU - Run Du
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2608.17963
UR - https://arxiv.org/abs/2608.17963
AB - 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.
ER -