Inequality constraint on the maximum genus for 3D structural compliance topology optimization

Area of Science:

• Engineering
• Computational Mechanics
• Materials Science

Background:

• Topology optimization is crucial for designing efficient structures.
• Controlling the number of holes (genus) is a key challenge in 3D topology optimization.
• Existing methods struggle to effectively constrain the genus in complex 3D structures.

Purpose of the Study:

• To propose a novel method, the quotient set design variable method (QSDV), for implementing inequality constraints on the maximum genus in 3D topology optimization.
• To demonstrate the effectiveness of the QSDV method in controlling topological features during structural optimization.
• To integrate the QSDV method with existing discrete variable topology optimization algorithms.

Main Methods:

• The quotient set design variable method (QSDV) classifies design variables based on element connectivity.
• The method updates elements within quotient sets to satisfy genus constraints.
• The QSDV is implemented within the discrete variable topology optimization method using a standard relaxation algorithm (DVTOCRA).

Main Results:

• The QSDV method successfully implements inequality constraints on the maximum genus.
• Numerical examples using a 3D cantilever beam demonstrate the effectiveness of the QSDV.
• The proposed method allows for precise control over the topological complexity of optimized structures.

Conclusions:

• The quotient set design variable method (QSDV) is an effective approach for genus constraint in 3D topology optimization.
• This method provides a robust way to manage the number of through-holes in optimized structures.
• The QSDV enhances the capabilities of topology optimization for complex engineering designs.