Topology Optimization of Periodic Structures Subject to Self-Weight Loading Using a Heuristic Method

Area of Science:

• Structural Mechanics
• Computational Engineering
• Materials Science

Background:

• Optimal design of periodic structures is challenging, especially with design-dependent loads.
• Existing methods often struggle with maintaining periodic patterns and connectivity.
• The field lacks comprehensive studies on topology optimization for periodic structures under these conditions.

Purpose of the Study:

• To present novel numerical optimization results for periodic structure topologies.
• To address the gap in research concerning design-dependent loads in periodic structures.
• To demonstrate an original approach combining topology optimization with periodic constraints.

Main Methods:

• Topology optimization formulation minimizing compliance subject to volume constraints.
• Application of Cellular Automata for material redistribution within the design domain.
• Numerical testing on 2D and 3D examples with various periodic schemes.

Main Results:

• Achieved optimized periodic structures without checkerboard effects or residual gray elements.
• Demonstrated the effectiveness of Cellular Automata for this specific optimization problem.
• Ensured inherent connectivity between periodic subdomains without additional constraints.

Conclusions:

• The proposed Cellular Automata-based topology optimization is effective for periodic structures.
• The method successfully handles design-dependent loads and maintains periodicity.
• This approach offers a robust solution for designing complex periodic materials and structures.