Normalized Field Product method for Topology Optimization

TL;DR

This paper introduces a parameter-free density evaluation method for topology optimization that naturally enforces length scale and produces mesh-independent, near-binary solutions without heuristics.

Contribution

It proposes a novel normalized product-based density evaluation method that is independent of user parameters and ensures pure 0-1 solutions in topology optimization.

Findings

Achieves mesh-independent, near-binary solutions

Imposes length scale implicitly on solid phase

Gradient vanishes at pure 0-1 topologies

Abstract

The paper presents a novel, parameter free, density evaluation method for topology optimization based on normalized product of a scalar field. The approach imposes length scale on solid phase implicitly and allows for pure 0-1 singularity free solutions to exist within the design space. The density formulation proposed herein is independent of user specified parameters, other then the length scale. Sensitivity analysis for the formulation obtained by combining the proposed density evaluation with the SIMP material model reveal that for compliance minimization and small deformation compliant mechanism problems, objective gradients vanish at pure 0-1 topologies. The methodology is implemented to solve well known examples in literature for different mesh refinements presenting mesh independent and close to binary solutions without the use of heuristics or continuation methods.