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

TL;DR

This paper introduces a parameter-free density evaluation method for topology optimization that produces near-binary designs with embedded length scale control, applicable to complex 2D and 3D problems without user intervention.

Contribution

A novel normalized field product approach that enforces minimum length scale and near-binary solutions in topology optimization without relying on traditional weight functions.

Findings

Successfully applied to 2D and 3D designs

Produces smooth, transition-free, near-binary topologies

Effective for both stiff structures and compliant mechanisms

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.