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A Quasi-Optimal Shape Design Method for Lattice Structure Construction

Sifan Chen, Yuan Kong, Qiang Zou

TL;DR

The paper tackles robust lattice structure construction by replacing complex nodal geometry with optimized, watertight nodal patches. It introduces a three-step workflow—optimal cutting, optimal nodal shape design via Grey Wolf optimization, and lattice stitching—to remove inter-strut intersections while preserving geometry, supplemented by multiresolution mesh generation. Quantitative results across 10 case studies show reduced shape deviation compared with prior methods and efficient GPU-enabled optimization, demonstrating improved robustness and practicality for downstream fabrication and simulation. The work advances lattice modeling by integrating meta-heuristic optimization into B-rep construction and providing a flexible, non-triangular-face lattice representation suitable for precise manufacturing.

Abstract

Lattice structures, known for their superior mechanical properties, are widely used in industries such as aerospace, automotive, and biomedical. Their advantages primarily lie in the interconnected struts at the micro-scale. The robust construction of these struts is crucial for downstream design and manufacturing applications, as it provides a detailed shape description necessary for precise simulation and fabrication. However, constructing lattice structures presents significant challenges, particularly at nodes where multiple struts intersect. The complexity of these intersections can lead to robustness issues. To address this challenge, this paper presents an optimization-based approach that simplifies the construction of lattice structures by cutting struts and connecting them to optimized node shapes. By utilizing the recent Grey Wolf optimization method -- a type of meta-heuristic method -- for node shape design, the approach ensures robust model construction and optimal shape design. Its effectiveness has been validated through a series of case studies with increasing topological and geometric complexity.

A Quasi-Optimal Shape Design Method for Lattice Structure Construction

TL;DR

The paper tackles robust lattice structure construction by replacing complex nodal geometry with optimized, watertight nodal patches. It introduces a three-step workflow—optimal cutting, optimal nodal shape design via Grey Wolf optimization, and lattice stitching—to remove inter-strut intersections while preserving geometry, supplemented by multiresolution mesh generation. Quantitative results across 10 case studies show reduced shape deviation compared with prior methods and efficient GPU-enabled optimization, demonstrating improved robustness and practicality for downstream fabrication and simulation. The work advances lattice modeling by integrating meta-heuristic optimization into B-rep construction and providing a flexible, non-triangular-face lattice representation suitable for precise manufacturing.

Abstract

Lattice structures, known for their superior mechanical properties, are widely used in industries such as aerospace, automotive, and biomedical. Their advantages primarily lie in the interconnected struts at the micro-scale. The robust construction of these struts is crucial for downstream design and manufacturing applications, as it provides a detailed shape description necessary for precise simulation and fabrication. However, constructing lattice structures presents significant challenges, particularly at nodes where multiple struts intersect. The complexity of these intersections can lead to robustness issues. To address this challenge, this paper presents an optimization-based approach that simplifies the construction of lattice structures by cutting struts and connecting them to optimized node shapes. By utilizing the recent Grey Wolf optimization method -- a type of meta-heuristic method -- for node shape design, the approach ensures robust model construction and optimal shape design. Its effectiveness has been validated through a series of case studies with increasing topological and geometric complexity.

Paper Structure

This paper contains 15 sections, 18 equations, 18 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Explicit Methods
  4. Implicit Methods
  5. Methods
  6. Problem Statement
  7. The Overall Workflow
  8. Optimal cutting
  9. Optimal nodal shape design
  10. Lattice stitching
  11. Multiresolution triangular mesh generation
  12. Results and Discussion
  13. Examples
  14. Discussion and Limitations
  15. Conclusion

Figures (18)

  • Figure 1: Illustration of the lattice graph representation, the B-rep model constructed, and the final fabricated object
  • Figure 2: A singular example (tangency) of boundary evaluation for a lattice node
  • Figure 3: The proposed lattice structure construction workflow
  • Figure 4: Minimum cutting length to avoid intersection with a pair of struts: (a) two struts with angle $> 90\degree$; and (b) two struts with angle $< 90\degree$
  • Figure 5: Optimal cutting: (a) data structure $PQ$ and $A$; (b) corresponding example of intersected struts; (c) result of optimal cutting; and (d) result of optimal cutting post-processing
  • ...and 13 more figures