Computer Methods in Applied Mechanics and Engineering - 2026

Topology optimization of additively manufactured continuous fiber-reinforced composites using B-spline components

A geometry-driven framework that concurrently optimizes structural topology, continuous fiber paths, path spacing, and fiber usage for additively manufactured composites.

Yifan Guo1, Jikai Liu3, Shuzhi Xu2,*, Kentaro Yaji2, Takayuki Yamada1,*
1 Department of Mechanical Engineering, The University of Tokyo, Japan
2 Department of Mechanical Engineering, The University of Osaka, Japan
3 School of Mechanical Engineering, Shandong University, China
* Corresponding authors
Paper PDF DOI Research Page Citation
Variable-width B-spline components and their continuous fiber-path fields

Variable-width B-spline components simultaneously describe the structural geometry, continuous fiber-path field, and spatially varying reinforcement allocation.

Abstract

This work proposes a B-spline-driven topology and fiber-path optimization framework for continuous fiber-reinforced composites. Multiple variable-width B-spline components represent the structural layout, while continuous fiber paths are generated as iso-contours of the component-induced scalar field. A separate spacing-control field enables local adjustment of fiber density and global control of fiber usage. Non-self-crossing, attachment, and fiber-content constraints improve path continuity and manufacturability. The optimized direction and fiber-density indicators are mapped to homogenized orthotropic material properties, and adjoint sensitivities are derived for all parametric variables.

Explicit B-spline geometry

Variable-width components provide compact topology control and direct CAD compatibility.

Continuous fiber paths

Printable trajectories are extracted directly from iso-contours of the optimized scalar field.

Fiber-content control

Local spacing and global fiber usage are adjusted within the same optimization framework.

Manufacturability aware

Geometric constraints prevent self-crossing and promote coherent component attachment.

Method

Each component contains a B-spline centerline, a variable radius field, and a spacing-control field. Their assembled scalar field defines the structural boundary and the continuous fiber trajectories. The local tangent direction and an analytically evaluated fiber-density indicator are then coupled with a homogenization-based constitutive model. The complete formulation optimizes geometry, reinforcement paths, and material allocation using a shared set of design variables.

Continuous fiber-path generation and homogenized material construction
Iso-contours generate continuous paths; their tangents and local density indicators define the orthotropic homogenized material response.
Non-self-crossing and attachment constraints for B-spline components
The non-self-crossing constraint removes degenerate centerlines, while the attachment constraint promotes smooth and coherent coupling between neighboring components.
Optimization workflow of the proposed method
The workflow integrates initialization, geometry and field construction, homogenized analysis, constraint evaluation, sensitivity analysis, and design-variable updates.

Numerical Results

MBB-beam, L-bracket, and compliant-mechanism benchmarks evaluate initialization, minimum feature size, component manufacturability, local fiber density, and global fiber usage. The examples show that the framework produces smooth structural skeletons together with continuous reinforcement paths and controllable spacing.

32.41% Maximum-displacement reduction in the stiffness-oriented verification cases
31.00% Average-displacement reduction compared with reference fiber layouts
2.46% Output-displacement gain from moderate reinforcement in the compliant mechanism
1.10% Gain of moderate reinforcement over the over-reinforced mechanism design
MBB beam initialization and optimization results
MBB-beam studies compare principal-stress-based initialization, component counts, optimized layouts, fiber paths, and convergence behavior.
L-bracket results under fiber-content constraints
L-bracket results demonstrate local fiber-density control, global fiber-budget control, and their influence on topology and reinforcement allocation.
Effects of B-spline manufacturability constraints
Minimum radius, non-self-crossing, and attachment constraints control feature size, eliminate invalid path interactions, and improve geometric coherence.
Compliant mechanism optimization results
Compliant-mechanism examples reveal the balance between fiber reinforcement and the flexibility needed to transmit the prescribed output motion.

Full-Scale Reconstruction and Verification

The explicit B-spline representation allows optimized boundaries to be reconstructed as CAD geometry without complex topology-repair procedures. Full-scale finite-element models retain the resolved matrix and fiber paths to assess the mechanical effectiveness of the optimized reinforcement. Stiffness-oriented cases substantially reduce both maximum and average displacement, while the compliant-mechanism study confirms that excessive fiber coverage can over-stiffen the structure.

Full-scale reconstruction of the optimized MBB beam
From B-spline boundary curves to the reconstructed CAD geometry and full-scale matrix-fiber finite-element model.

Citation

@article{guo2026bsplinefiber,
  title   = {Topology optimization of additively manufactured continuous
             fiber-reinforced composites using B-spline components},
  author  = {Guo, Yifan and Liu, Jikai and Xu, Shuzhi and Yaji, Kentaro
             and Yamada, Takayuki},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume  = {461},
  pages   = {119224},
  year    = {2026},
  doi     = {10.1016/j.cma.2026.119224}
}

Acknowledgements

This work was supported in part by JSPS KAKENHI Grant Numbers JP23H03800, JP25H01108, and 25KF0244.