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The Semi-Penalized Updated Properties Model and Its Algorithm to Impose the Volume Fraction.

Amin Alibakhshi1, Luis Saucedo-Mora1

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A new topology optimization method, the Updated Properties Model (UPM), now incorporates volume constraints without complex formulations. This allows for efficient design of lightweight, stiff structures using additive manufacturing.

Keywords:
density-dependent Young modulustopology optimizationupdated properties modelsvolume constraint

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Area of Science:

  • Engineering
  • Materials Science
  • Computational Mechanics

Background:

  • Topology optimization is crucial for designing efficient structures for additive manufacturing.
  • Existing methods often require complex constraint-handling formulations.
  • The Updated Properties Model (UPM) previously optimized structures without explicit constraints.

Purpose of the Study:

  • To extend the constraint-free UPM algorithm to incorporate volume fraction constraints.
  • To achieve constraint-aware topology optimization without complex constraint-handling.
  • To enable controlled material distribution in optimized structures.

Main Methods:

  • Incorporated volume fraction using a density-dependent Young modulus concept within the UPM.
  • Utilized strain homogenization as the objective function and updating Young modulus as the design variable.
  • Tested the methodology on 2D and 3D benchmark structures.

Main Results:

  • The proposed UPM successfully replicated constraint-driven outcomes without explicit constraint enforcement.
  • Algorithmic parameter adjustments yielded both binary (single-material) and graded-material solutions.
  • Demonstrated the algorithm's functionality and success in benchmark tests.

Conclusions:

  • The extended UPM framework allows for controlled material distribution through a physically meaningful update rule.
  • This approach enhances the applicability of topology optimization for engineering designs.
  • A Julia package has been developed to facilitate the use of the proposed UPM method.