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

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.