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

2025-07-25

AI Summary

Addressing the challenge of simultaneously achieving structural performance and manufacturability in two-dimensional topology optimization, this paper proposes a multi-thickness density-based optimization method. The approach integrates hierarchical penalization, smoothed Heaviside projection, parameter continuation, and adaptive mesh refinement to effectively suppress spurious thin features. With only three discrete thickness levels, it closely approximates the performance of continuous thickness-varying designs. The method inherently accommodates both additive manufacturing and conventional machining constraints, significantly enhancing convergence stability and geometric resolution. Benchmark tests on cantilever and MBB beams demonstrate compliance errors below 2% and stiffness values nearly matching those of variable-thickness optimization—substantially outperforming the standard SIMP method in both accuracy and manufacturability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Balancing structural performance and manufacturability in topology optimization
• Bridging gap between variable-thickness and penalized (SIMP) methods
• Ensuring designs meet discrete thickness constraints for practical fabrication

Innovation

• Multi-thickness density-based topology optimization method
• Multilevel penalization and smoothed Heaviside projection
• Adaptive mesh refinement for robust convergence