Normalized field product approach: A parameter-free density evaluation method for close-to-binary solutions in topology optimization with embedded length scale

2024-12-24

AI Summary

To address challenges in topology optimization—including difficulty in achieving near-binary designs, reliance on empirical parameters for minimum feature-size control, and boundary staircasing—this paper proposes a parameter-free, near-binary topology optimization method. The method introduces a normalized field-product density function, integrated with the SIMP stiffness interpolation scheme, to implicitly embed the minimum length scale for solid phases without requiring weighting functions or user-tuned parameters. Coupled with volume-conserving smoothing and higher-order element extension techniques, it ensures that the density field automatically satisfies prescribed feature-size constraints. The approach consistently yields high-quality, near-binary designs with smooth boundaries and enhanced robustness in both 2D and 3D applications, including rigid structural and compliant mechanism optimization. Numerical experiments demonstrate significant improvements in manufacturability and numerical stability compared to conventional methods.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

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• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

This paper provides a normalized field product approach for topology optimization to achieve close-to-binary optimal designs. The method employs a parameter-free density measure that implicitly enforces a minimum length scale on the solid phase, allowing for smooth and transition-free topologies. The density evaluation does not rely on weight functions; however, the related density functions must have values between 0 and 1. The method combines the SIMP scheme and the introduced density function for material stiffness interpolation. The success and efficacy of the approach are demonstrated for designing both two- and three-dimensional designs, encompassing stiff structures and compliant mechanisms. The structure's compliance is minimized for the former, while the latter involves optimizing a multi-criteria objective. Numerical examples consider different volume fractions, length scales, and density functions. A volume-preserving smoothing and resolution scheme is implemented to achieve serrated-free boundaries. The proposed method is also seamlessly extended with advanced elements for solving 3D problems. The optimized designs obtained are close to binary without any user intervention while satisfying the desired feature size on the solid phase.

Problem

• Topology Optimization
• Binarization
• Material States

Innovation

• Topology Optimization
• Density Function
• Boundary Smoothing