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

Summary

A novel density evaluation method, called the normalized field product (nFP) approach, is proposed for topology optimization. It achieves close-to-binary solutions without user-defined parameters or weight functions. The method is demonstrated on 2D and 3D stiff structures and compliant mechanisms, showing its effectiveness and versatility.

Highlights

• The nFP approach is a parameter-free density evaluation method for topology optimization.
• It achieves close-to-binary solutions without user intervention or continuation schemes.
• The method is demonstrated on 2D and 3D stiff structures and compliant mechanisms.
• The nFP approach is shown to be mesh-independent and can handle different volume fractions and length scales.
• The method can be extended to 3D problems with advanced elements, such as truncated octahedron elements.
• The nFP approach is compared to the Heaviside projection method, showing its advantages.
• The method's convergence and grayness measure characteristics are analyzed.

Key Insights

• The nFP approach provides a novel way to evaluate densities in topology optimization, eliminating the need for user-defined parameters or weight functions. This makes the method more robust and easy to use.
• The method's ability to achieve close-to-binary solutions without user intervention or continuation schemes is a significant advantage over existing methods. This reduces the complexity of the optimization process and makes it more efficient.
• The nFP approach is versatile and can be applied to various topology optimization problems, including 2D and 3D stiff structures and compliant mechanisms. This makes it a valuable tool for engineers and researchers in the field.
• The method's mesh-independence is a critical feature, as it allows for consistent results regardless of the mesh size or refinement. This reduces the computational cost and makes the method more practical for large-scale problems.
• The nFP approach can handle different volume fractions and length scales, making it suitable for a wide range of applications. This flexibility is essential in topology optimization, where the goal is to find the optimal design for a specific problem.
• The extension of the nFP approach to 3D problems with advanced elements, such as truncated octahedron elements, is a significant contribution. This enables the method to be applied to complex 3D problems, which are common in engineering and architecture.
• The comparison between the nFP approach and the Heaviside projection method highlights the advantages of the proposed method. The nFP approach is shown to be more efficient and robust, making it a better choice for topology optimization problems.

Mindmap

Citation

Singh, N., Kumar, P., & Saxena, A. (2024). Normalized field product approach: A parameter-free density evaluation method for close-to-binary solutions in topology optimization with embedded length scale (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.18441