A novel multi-thickness topology optimization method for balancing structural performance and manufacturability

TL;DR

This paper presents a multi-thickness topology optimization method that balances structural performance with manufacturability by guiding designs toward discrete thickness levels using novel penalization and projection techniques.

Contribution

It introduces a multilevel penalization scheme and smoothed Heaviside projection to produce high-performance, manufacturable designs with discrete thicknesses, bridging the gap between variable and penalized TO methods.

Findings

Designs with three thickness levels achieve near-optimal compliance.

The method outperforms standard SIMP in structural performance.

Designs are suitable for additive manufacturing and traditional fabrication.

Abstract

Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods producing simpler, truss-like structures with compromised performance. This paper introduces a multi-thickness, density-based topology optimization method designed to bridge this gap. The proposed approach guides the design towards a predefined set of discrete, allowable thicknesses by employing a novel multilevel penalization scheme and a multilevel smoothed Heaviside projection. A continuation strategy for the penalization and projection parameters, combined with an adaptive mesh refinement technique, ensures robust convergence and high-resolution geometric features. The method is validated on standard cantilever and MBB beam benchmarks. Results demonstrate that as the number of allowable thicknesses increases, the designs systematically transition from conventional truss-like structures to high-performance, sheet-like structures. Notably, designs with as few as three discrete thickness levels achieve compliance values within 2\% of those from fully unpenalized, variable-thickness optimization, while significantly outperforming standard SIMP results. The method inherently eliminates impractically thin regions and features, both in the out-of-plane and in-plane directions and produces designs well-suited for both additive manufacturing and conventional fabrication using standard-thickness stock materials, thus maximizing both performance and manufacturability.