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Three-Dimensional Multi-Material Topology Optimization: Applying a New Mapping-Based Projection Function.

Hélio Luiz Simonetti1, Francisco de Assis das Neves2, Valério Silva Almeida3

  • 1Department of Mathematics, Federal Institute of Education, Science and Technology of Minas Gerais (IFMG), Betim 32677-562, Brazil.

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Summary

This study introduces efficient MATLAB code for 3D multi-material topology optimization. The new sigmoid projection function enhances computational efficiency and improves results compared to previous methods.

Keywords:
3D structuresMATLAB codemulti-materialsigmoid functiontopology optimization

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Area of Science:

  • Engineering
  • Computational Mechanics
  • Materials Science

Background:

  • Topology optimization is crucial for designing efficient structures.
  • Multi-material design presents challenges in achieving clear, manufacturable results.
  • Existing methods may lack computational efficiency and optimal performance.

Purpose of the Study:

  • To develop an efficient and compact MATLAB code for 3D multi-material topology optimization.
  • To introduce a novel sigmoid projection function for improved design variable filtering.
  • To demonstrate enhanced computational efficiency and objective function performance.

Main Methods:

  • Utilized a mapping-based material interpolation function for multi-material problems.
  • Implemented a sigmoid projection function for filtered design variables.
  • Performed sensitivity analysis and presented a detailed optimization model.

Main Results:

  • Achieved computational cost reduction of up to 36.7%.
  • Improved the objective function by 19.1% compared to the hyperbolic tangent function.
  • Generated clear 0/1 material distribution without gray elements, facilitating manufacturing.

Conclusions:

  • The developed MATLAB code offers an efficient solution for 3D multi-material topology optimization.
  • The sigmoid projection function significantly enhances computational efficiency and solution quality.
  • Numerical examples validate the code's effectiveness and demonstrate the impact of support placement.