Flexible fiber studied in fluid flow using a variational method

The interaction between flexible bodies and fluids is very complex, however, studying this mechanism helps us understand how natural plants deform in response to fluid flow to prevent structural damage. Due to the complexity of fluid-structure interaction, there is a lack of methods for quickly and quantitatively calculating the deformation and drag of flexible body systems. In this paper, the principles of variational methods are used to solve for the deformation shape and drag of a flexible fiber in a flowing fluid. The deformation shape of the fiber is treated as the primary unknown, leading to the derivation of an approximate variational equation. The results are in good agreement with those obtained from CFD methods, while requiring fewer computational resources. In terms of specific methods, the differential equation corresponding to the steady-state solution of this problem is transformed into an approximate variational equation, and parameters are adjusted by comparing it with the results of numerical simulation. Some quantitative theoretical solutions are provided, and the relevant laws are summarized. The law of drag variation is described through dimensionless velocity and drag. It is found that the nonconstant-cross-section stiffness fiber with thick fixed ends and slender free ends is more effective in preventing structural damage when facing incoming flow compared with the constant-cross-section stiffness fiber. This is manifested by the reduction of maximum stress and the movement of the position of maximum stress with the flow velocity.