An Advection-Diffusion based Filter for Machinable Designs in Topology Optimization

TL;DR

This paper presents a novel advection-diffusion based filtering method for topology optimization that ensures manufacturability, is computationally efficient, easy to implement on unstructured meshes, and effective for large-scale problems.

Contribution

It introduces a new filtering approach using the advection-diffusion equation with Robin boundary conditions, improving efficiency and simplicity over traditional methods.

Findings

Efficient filtering on unstructured meshes with up to 64 million elements.

Applicable to multiple milling tool directions without extensive parameter tuning.

Reduced computational cost compared to traditional filtering methods.

Abstract

This paper introduces a simple formulation for topology optimization problems ensuring manufacturability by machining. The method distinguishes itself from existing methods by using the advection-diffusion equation with Robin boundary conditions to perform a filtering of the design variables. The proposed approach is less computationally expensive than the traditional methods used. Furthermore, the approach is easy to implement on unstructured meshes and in a distributed memory setting. Finally, the proposed approach can be performed with few to no continuation steps in any system parameters. Applications are demonstrated with topology optimization on unstructured meshes with up to 64 million elements and up to 29 milling tool directions.