Global-Local Airframe FEA

What Is It?

Global-local airframe FEA is the modelling methodology where a global model of the entire airframe (or a major component) is used to determine the overall load distribution, and local models of specific details are used to determine the local stress and failure margin. The global model captures the overall structural behaviour — the bending, shear, torsion and the load flow through the major components. The local model captures the detailed stress at a specific location — a joint, a cut-out, a fitting, a fastener hole. The two models are connected: the global model provides the boundary conditions and loads for the local model. This global-local approach is the standard methodology for airframe structural analysis.

Why It Matters

A single model cannot capture both the global load distribution and the local stress efficiently. A global model that is fine enough to resolve a fastener hole would have billions of degrees of freedom — impractical. A local model that captures a fastener hole but is not connected to the global load distribution has unknown boundary conditions — the loads are guessed. The global-local approach resolves this: the global model is coarse (beam and shell elements, reasonable mesh) and captures the overall loads; the local model is fine (solid elements, detailed geometry, fastener holes) and captures the local stress, with boundary conditions from the global model. This is the only practical way to analyse an airframe structure at the level of detail required for substantiation.

The global model finds where the load goes; the local model determines what that load does to the detail. Neither is sufficient alone. The global model without local detail misses the stress concentrations; the local model without global context has unknown loads. The two must be connected.

The Global Model

The global model represents the entire airframe or a major component (wing, fuselage). It uses beam, shell and occasionally solid elements to represent the major structural members — spars, ribs, skins, frames, stringers. The mesh is coarse by local standards — element sizes of tens of millimetres to hundreds of millimetres — but sufficient to capture the overall load distribution. The global model is used to compute the internal loads — the bending, shear, torsion and axial forces throughout the structure — under the applied external loads. It identifies the critical locations — where the loads are highest, where the stress concentrations are expected, where the local detail models are needed.

• Overall stiffness and load distribution
• Internal loads: bending, shear, torsion, axial throughout the structure
• Boundary conditions: external loads, supports, interfaces
• Major structural members: spars, ribs, skins, frames, stringers
• Element types: beam (spars, stringers), shell (skins, webs), occasional solid (fittings)

The Local Model

The local model represents a specific detail — a joint, a cut-out, a fitting, a fastener hole, a ply drop in a composite. It uses solid elements and a fine mesh to resolve the local stress concentrations. The geometry is detailed — the hole, the fillet, the fastener, the laminate lay-up are all explicitly represented. The boundary conditions come from the global model — the displacements or forces at the boundary of the local model are extracted from the global model and applied to the local model. The local model computes the detailed stress field and the failure margin at the critical location.

Submodelling

Submodelling is the technique that connects the global model to the local model. The global model is run first, and the displacements at the boundary of the local region are extracted. These displacements are applied as boundary conditions to the local model — the local model is "driven" by the global model. The local model, with its fine mesh and detailed geometry, then computes the local stress field under these boundary conditions. Submodelling can be performed at multiple levels — a global model, a intermediate submodel of a wing section, and a detailed submodel of a specific joint. Each level refines the detail from the level above.

Submodelling hierarchy:

Global airframe model (beam/shell, coarse)
  → identify critical wing-root region
  → extract displacements at submodel boundary

Wing-root submodel (shell/solid, medium)
  → resolve load distribution at root
  → identify critical joint
  → extract displacements at joint boundary

Joint detail model (solid, fine, with fastener holes)
  → resolve local stress at hole
  → compute failure margin

Load Extraction and Free-Body Cuts

An alternative to displacement-based submodelling is load extraction. The global model is used to extract the forces and moments at a "free-body cut" — a section through the structure at the boundary of the local model. These forces and moments are then applied as loads to the local model. The free-body cut approach is useful when the displacement field at the boundary is complex or when the local model needs to be run with different load cases extracted from the global model. The loads at the free-body cut must be in equilibrium — the forces and moments must balance the external loads on the portion of the structure represented by the local model.

Beam-Shell-Solid Hierarchy

The element type hierarchy — beam, shell, solid — corresponds to the structural scale. Beams represent slender members (spars, stringers, longerons) where the cross-section is small compared to the length — the beam carries axial, bending, shear and torsion through cross-sectional properties. Shells represent thin walls (skins, webs) where the thickness is small compared to the other dimensions — the shell carries membrane and bending loads through the shell formulation. Solids represent thick or complex regions (fittings, joints, fastener holes) where the full 3D stress state must be resolved. The global model is dominated by beams and shells; the local model is dominated by solids. The transition between element types — beam to shell, shell to solid — must be handled carefully to avoid artificial stress concentrations at the interface.

Key Takeaways

• Global-local FEA connects a coarse global model to a fine local model for efficient airframe analysis
• The global model finds the load distribution; the local model finds the local stress
• Submodelling transfers displacements from the global model as boundary conditions for the local model
• Free-body cuts extract forces and moments from the global model for the local model loads
• The beam-shell-solid hierarchy corresponds to the structural scale