An efficient NURBS-based reconstruction approach to isogeometric analysis of triply periodic minimal surface structures

KD Nguyen and TV Duong and JH Lee and Y Bazilevs and H Nguyen-Xuan, ENGINEERING WITH COMPUTERS, 41, 4479-4509 (2025).

DOI: 10.1007/s00366-025-02206-z

Triply periodic minimal surfaces (TPMS) are of increasing interest in various fields due to their unique structural and functional porous material properties. In this paper, we present a novel approach for reconstructing TPMS structures using non-uniform rational B-splines (NURBS). A balancing composite motion optimization (BCMO) algorithm is leveraged to optimize control points and weights. Using the inherent periodicity of TPMS, the optimization process is simplified by focusing on a single surface patch, from which the complete structure is generated through rotations and reflections. Despite using low-degree NURBS basis functions, the reconstructed surfaces demonstrate reasonable accuracy compared to the exact TPMS geometry. The proposed method significantly reduces the number of control points required compared to the isosurface approach. The new surface enables computationally efficient analysis via multi-patch isogeometric analysis (IGA) for both shells and solids. Additionally, the present method shows robust performance for a wide variety of TPMS types, eliminating the necessity for computationally intensive re-optimization.

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