[Paper Review] Self-support topology optimization considering distortion for metal additive manufacturing

Takao Miki|arXiv (Cornell University)|Aug 30, 2022

Topology Optimization in Engineering4 citations

TL;DR

This paper proposes a level-set-based topology optimization method for metal additive manufacturing that integrates self-support constraints and distortion suppression via thermal and mechanical models. By combining overhang angle control, heat dissipation optimization, and inherent strain-based distortion prediction, the method produces support-free, high-precision parts with minimal distortion and overheating, validated through 2D and 3D numerical examples with up to 112% of reference thermal compliance.

ABSTRACT

This paper proposes a self-support topology optimization method that considers distortion to improve the manufacturability of additive manufacturing. First, a self-support constraint is proposed that combines an overhang angle constraint with an adjustable degree of the dripping effect and a thermal constraint for heat dissipation in the building process. Next, we introduce a mechanical model based on the inherent strain method in the building process and propose a constraint that can suppress distortion. An optimization problem is formulated to satisfy all constraints, and an optimization algorithm based on level-set-based topology optimization is constructed. Finally, two- and three-dimensional optimization examples are presented to validate the effectiveness of the proposed topology optimization method.

Motivation & Objective

• To develop a self-support topology optimization method that eliminates the need for support structures in laser powder bed fusion (LPBF) metal additive manufacturing.
• To address distortion and overheating—key manufacturing defects in LPBF—by integrating thermal and mechanical constraints into the optimization framework.
• To ensure manufacturability by enforcing overhang angle limits while minimizing structural performance loss.
• To enable support-free, high-precision parts through a unified optimization framework that combines geometric, thermal, and mechanical constraints.
• To validate the method’s effectiveness through 2D and 3D numerical examples with quantitative comparisons of distortion, overheating, and compliance.

Proposed method

• Proposes a Helmholtz-type PDE with adjustable parameters to control downward convex shapes, enabling explicit overhang angle constraints via angle vector formulation.
• Introduces a thermal constraint based on heat dissipation in each layer, formulated as a domain integral to maximize thermal conductivity and suppress overheating.
• Develops a mechanical model using the inherent strain method to predict and suppress distortion during the layer-by-layer building process.
• Constructs an optimization algorithm using the level-set method with finite element method (FEM) for solving the constrained problem.
• Implements penalty-based constraints by embedding the self-support, thermal, and distortion constraints into the objective function with adjustable penalty parameters.
• Uses a two-step validation approach: 2D examples to tune parameters and 3D examples to demonstrate manufacturability and performance under real process conditions.

Experimental results

Research questions

• RQ1 Can a self-support topology optimization method effectively eliminate overhanging regions without relying on support structures in LPBF?
• RQ2 How can thermal constraints be formulated to suppress overheating and improve heat dissipation during the building process?
• RQ3 To what extent can the inherent strain method be used to predict and minimize distortion in metal AM parts?
• RQ4 What is the trade-off between structural performance (e.g., thermal compliance) and manufacturability when applying multiple constraints?
• RQ5 Can the proposed method produce support-free parts with minimal distortion and overheating in 3D complex geometries?

Key findings

• The self-support constraint successfully eliminated overhanging regions in 2D and 3D examples, with no violation of the 45° overhang angle threshold.
• The thermal constraint reduced overheating by promoting heat dissipation, as confirmed by peak temperature comparisons showing lower thermal gradients.
• The distortion constraint led to a more uniform distortion distribution, reducing localized deformation in the 3D heat conduction model.
• The optimized 3D heat conduction part with both self-support and distortion constraints achieved a thermal compliance of 112% of the reference (Jp/Jpref = 112%), indicating minimal performance degradation.
• The method produced a support-free design with suppressed distortion and overheating, demonstrating feasibility for high-precision, supportless AM manufacturing.
• Parameter tuning via 2D examples enabled consistent performance in 3D cases, showing that the method is robust across different problem settings.