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Flexible fiber studied in fluid flow using a variational method.

Haoyu Liu1, Edidiong Michael Umana1, Xiufeng Yang1

  • 1Beijing Institute of Technology, Department of Mechanics, Beijing 100081, China.

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|April 18, 2026
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Summary
This summary is machine-generated.

This study introduces a variational method to calculate flexible fiber deformation and drag in fluid flow, offering a faster alternative to CFD. Non-constant stiffness fibers better prevent structural damage from fluid forces.

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Area of Science:

  • Fluid Dynamics
  • Solid Mechanics
  • Biophysics

Background:

  • Fluid-structure interaction (FSI) is complex, hindering quantitative analysis of flexible body deformation and drag.
  • Understanding plant deformation in fluid flow is crucial for preventing structural damage.

Purpose of the Study:

  • To develop a computationally efficient method for calculating the deformation and drag of flexible fibers in fluid flow.
  • To investigate the structural integrity of fibers with varying stiffness under fluidic stress.

Main Methods:

  • Applied variational principles to derive an approximate variational equation for fiber deformation.
  • Transformed the steady-state differential equation into an approximate variational equation.
  • Adjusted parameters by comparing with numerical simulation results.

Main Results:

  • The variational method showed good agreement with Computational Fluid Dynamics (CFD) results but required fewer resources.
  • Developed quantitative theoretical solutions and summarized drag variation laws using dimensionless velocity and drag.
  • Identified non-constant cross-section stiffness fibers (thick ends, slender free ends) as superior for damage prevention compared to constant-section fibers.

Conclusions:

  • The developed variational method provides an efficient approach to FSI problems involving flexible bodies.
  • Non-constant stiffness design significantly enhances structural resilience against fluid flow by reducing maximum stress and shifting its location.