fea-fluid-structure

name	fea-fluid-structure
description	Fluid-structure interaction (FSI) FEA — ALE formulation, added mass, one-way vs. two-way coupling, vortex-induced vibration, hydroelastic flutter, aeroelastic divergence, ABAQUS/ANSYS/OpenFOAM coupling, pressure mapping.
metadata	{"priority":7,"promptSignals":{"phrases":["fluid structure interaction","FSI analysis","aeroelastic","hydroelastic","ALE formulation","added mass FEA"],"minScore":3}}

Fluid-Structure Interaction (FSI) FEA — Complete Skill

FSI Classification

One-Way (Uncoupled) FSI

Method: CFD → extract pressure field → apply as load to FEA (no feedback) Applicable when: structural deformation << fluid domain scale; deformation does not significantly change fluid flow Examples: static pressure loading on aircraft panel; wind load on building facade; pump impeller under steady pressure Workflow: CFD (OpenFOAM/ANSYS Fluent) → pressure file → FEA (ABAQUS/ANSYS) surface pressure load Interpolation: nearest-neighbor or RBF (radial basis function) mapping of pressure from CFD mesh to FEA mesh

Two-Way (Coupled) FSI

Method: fluid and structure solvers exchange pressure, displacement, velocity iteratively each time step Applicable when: structural deformation significantly affects flow (flutter, large-deflection membranes, biological valves) Examples: heart valve; bridge flutter; compliant pipe; flexible wing at high angle of attack Coupling methods:

• Partitioned: separate fluid (CFD) + structure (FEA) solvers with data exchange at interface
• Monolithic: single solver matrix for fluid+structure DOF (more stable but expensive)

Arbitrary Lagrangian-Eulerian (ALE) Formulation

Problem with pure Lagrangian (FEA mesh follows material): mesh distorts severely with large fluid deformation Problem with pure Eulerian (CFD fixed mesh): material interface tracking difficult

ALE solution: mesh moves arbitrarily (neither with material nor fixed); decouple mesh motion from material motion ALE governing equation (convective form): ρ(∂v/∂t|_χ + (v - v̂)·∇v) = ∇·σ + ρb χ = ALE reference coordinate; v̂ = mesh velocity; (v - v̂) = convective velocity

Mesh motion strategies:

• Laplacian smoothing: solve ∇²x_mesh = 0 in fluid domain; maintains mesh quality
• Spring analogy: mesh elements as springs; stiffer near boundaries
• Remeshing: when quality degrades below threshold → interpolate fields to new mesh

ABAQUS ALE adaptive meshing: *ADAPTIVE MESH CONTROLS; use for impact and large-deformation problems

Added Mass Effect

Phenomenon: fluid resists acceleration of submerged structure → effective mass increases Added mass coefficient C_a (potential flow):

• Circular cylinder (transverse): m_a = C_a × ρ_f × π/4 × D² × L; C_a = 1.0 (theory)
• Sphere: m_a = C_a × ρ_f × (2/3)π r³; C_a = 0.5
• Flat plate (normal): C_a ≈ (π/4) × D²/L (aspect ratio dependent)

Effect on natural frequency: ω_wet = ω_dry / √(1 + m_a/m_structure) For submerged pipe: f_wet / f_dry ≈ 0.5–0.8 depending on fluid/structure density ratio

Implementation: add mass matrix M_added = C_a × ρ_f × V_displaced to structural mass matrix

Vortex-Induced Vibration (VIV)

Strouhal number: St = f_s × D / U_∞ [f_s = vortex shedding frequency; D = diameter; U = free stream velocity] St ≈ 0.2 for circular cylinder (Re = 1000–10⁵)

Lock-in condition: when f_s ≈ f_n (structural natural frequency) → resonance → large amplitude vibration Lock-in range: 0.7 ≤ U_r ≤ 1.4 [U_r = U/(f_n × D) = reduced velocity]

Amplitude at lock-in: A/D ≈ 1.0 for lightly damped cylinders in air; A/D ≈ 0.5–0.8 for water Scrutan number: Sc = 2m_eff × ζ / (ρ_f × D²) [controls VIV amplitude; Sc > 50 → no significant VIV]

FEA-CFD coupling for VIV:

1. Start CFD with stationary cylinder → extract forces
2. Apply forces to structural FEA → compute displacement
3. Update CFD mesh to match structural displacement
4. Repeat each time step (typical dt = 0.01 × period)

Hydroelastic Flutter

Critical flutter velocity (panel in flow): U_flutter = U_divergence / √2 [approximate for 2D panel] Flutter condition: coupled bending-torsion mode → imaginary part of frequency eigenvalue becomes zero

Theodorsen function approach (2D airfoil flutter): Matrix: [M]{ẍ} + [C]{ẋ} + [K]{x} = q_dyn × [A(k)]{x} [k = reduced frequency = ωb/U] p-k method or v-g method to find flutter speed and flutter frequency

Hydroelastic divergence: Divergence: static instability; elastic restoring moment < hydrodynamic moment q_divergence = 1/2 × ρ × U² → K_T / (∂C_L/∂α) × (∂α/∂δ)⁻¹

ABAQUS/ANSYS FSI Coupling

ABAQUS + ABAQUS/CFD (co-simulation): *CO-SIMULATION: link ABAQUS structural + CFD solver Interface: *CO-SIMULATION REGION; fluid-structure boundary Exchange: displacement (structure → fluid); pressure/traction (fluid → structure) Staggered scheme: structure predictor → fluid correction → update

ANSYS Mechanical + ANSYS Fluent (System Coupling): Workbench: drag Structural and Fluid components into System Coupling cell Interface: Named Selection at FSI surface; auto-mapping of pressure and displacement Explicit (1-way) or implicit (2-way) coupling; subcycling allowed

OpenFOAM + structural solver (FEniCS/Code_Aster): preCICE coupling library: surface mesh exchange; RBF interpolation; convergence monitoring solidDisplacementFoam + FSI adapter for OpenFOAM solid solver

Pressure Mapping (One-Way)

CFD to FEA pressure transfer:

1. Extract pressure on FSI surface from CFD (surface mesh)
2. Interpolate to FEA mesh (different node locations)
3. Apply as distributed pressure load in FEA

Interpolation methods:

• Nearest node: fast; inaccurate for coarse-to-fine mapping
• RBF (radial basis function): accurate; handles non-matching meshes; computationally expensive
• Consistent pressure interpolation: preserve total force: F_FEA = ∑ p_FEA × A_FEA ≈ F_CFD

ABAQUS pressure loading: *DSLOAD, OP=NEW: apply distributed surface load Normal mapping: MAP SOLUTION between CFD and FEA (ABAQUS mapping tool)

Convergence and Stability

Partitioned coupling stability: Strongly coupled: use Aitken relaxation to accelerate convergence: ω = ω_old × r_old/(r_old - r_new) [r = residual] Weak coupling: explicit (one exchange per time step) → unstable for ρ_fluid ≈ ρ_structure (added mass instability)

Time step for explicit FSI: Δt_FSI ≤ min(Δt_fluid_CFL, Δt_structure_CFL, Δt_interface) For implicit: Δt can be larger; stability via Newton iteration within each time step

Convergence criterion: Displacement residual: ||x_new - x_old|| / ||x_new|| < 10⁻⁴ Force residual: ||F_fluid - F_structure|| / ||F_fluid|| < 10⁻³

Validation Benchmarks

Turek-Hron FSI benchmark: flexible beam behind square cylinder; well-documented; compare tip displacement and frequency NACA airfoil flutter: compare computed flutter speed to linear theory Circular cylinder VIV: compare A/D vs. reduced velocity to Gopalkrishnan (1993) data

Standards

Standard	Scope
ASME V&V 10	Verification and validation in computational solid mechanics
ASME V&V 20	V&V for CFD
ISO 7626	Mechanical vibration — structural dynamics measurements
ASME PTC 19.3	Temperature measurement in flow

Output

Provide: FSI type (one-way/two-way), coupling method (partitioned/monolithic), mesh motion scheme (ALE/remeshing), structural solver (ABAQUS/ANSYS), fluid solver (ANSYS Fluent/OpenFOAM), time step Δt [s] and number of coupling iterations per step, maximum structural displacement [mm], critical flutter velocity U_flutter [m/s] (if applicable), VIV lock-in check (reduced velocity U_r and Scrutan number Sc), added mass ratio m_a/m_structure, peak pressure on FSI surface [MPa], pressure mapping error (force balance check [%]), convergence achieved (displacement residual), and applicable standard (ASME V&V 10, V&V 20).