Loads & Load Application in FEA

APPLY THE PHYSICS, NOT JUST THE NUMBER

A load in FEA is defined by three things: its magnitude, its location, and its distribution. The magnitude is usually the easiest to determine — it comes from the load envelope, the test specification, the certification requirement. The location is usually straightforward — it comes from the geometry and the load path. The distribution is the part that is most often simplified, most often guessed, and most often wrong. A point load and a distributed load with the same resultant, applied at the same location, produce completely different stress fields. The point load produces a singularity; the distributed load produces a finite, convergent stress. The difference between the two is the difference between a meaningful stress result and a meaningless number.

Before applying a load, ask: how is this load actually transferred to the structure in reality? Is it a point contact, a line contact, a surface pressure, a body force? The model should represent the real distribution, not just the resultant.

Point Loads

A point load applies a force at a single node. It is the simplest load to apply and the most physically unrealistic. No real load is applied at a mathematical point — even a needle tip transfers force over a small area. In FEA, a point load creates a stress singularity: the stress at the loaded node increases without bound as the mesh is refined, because the force is divided by an element area that shrinks to zero. The stress at the loaded node is not a real stress; it is a numerical artefact. Point loads are acceptable only when the region of interest is far enough from the load application point for Saint-Venant's principle to apply, or when the load is applied to a non-design region (a loading pad, a bolt head) where the local stress is not of interest.

• Singularity: stress at the loaded node increases without bound with mesh refinement
• Acceptable when: region of interest is far from the load (Saint-Venant applies)
• Acceptable when: load is on a non-design region where local stress is not of interest
• Not acceptable when: the stress at the load point is the result being reported

Distributed Loads and Pressure

A distributed load applies force per unit length (shell edge) or per unit area (shell face or solid surface). A pressure applies force per unit area normal to the surface. Distributed loads and pressures are the natural representation of real loads: wind pressure on a panel, hydrostatic pressure on a tank wall, contact pressure on a bearing surface. They do not create singularities because the force is spread over a finite area. The stress at the loaded surface is finite and converges with mesh refinement. The choice between a uniform distribution and a non-uniform distribution (e.g., a cosine-bearing distribution on a pin hole) depends on the physics of the load transfer.

• Uniform pressure: simplest, appropriate for uniformly distributed loads (fluid pressure, wind)
• Linearly varying pressure: hydrostatic, varying bearing pressure
• Bearing distribution: cosine or sine distribution on a cylindrical hole — represents pin contact
• General distribution: mapped from CFD, test data, or a higher-fidelity analysis

Bearing Loads

A bearing load is the pressure distribution between a pin, bolt, or shaft and the hole or bore it contacts. The distribution is not uniform — it is concentrated on the side of the hole where the pin pushes, and varies from maximum at the centreline to zero at the edges of contact. A common idealisation is a cosine distribution: pressure proportional to the cosine of the angle from the load direction, applied over the contact half. This is a reasonable approximation for a clearance-free pin under radial load. For a bolted joint with clearance, preload, and friction, the distribution is more complex and may require a contact analysis to resolve. The key point is that a uniform pressure on a hole is rarely the right representation — it overestimates the stress at the edges and underestimates it at the centreline.

• Cosine bearing: pressure ∝ cos(θ), applied over the contact half — standard idealisation for clearance-free pin
• Sine bearing: pressure ∝ sin(θ) — alternative distribution, sometimes used for snug-fit pins
• Contact analysis: resolve the actual distribution by modelling pin-to-hole contact — highest fidelity, highest cost
• Uniform pressure: rarely correct — use only for rough estimates or when the distribution is genuinely unknown

bush-load-introduction

Inertia, Acceleration, and Gravity

Inertia loads are body forces applied to every element in the model: F = m·a for each element, where the mass comes from the element's volume and material density. Acceleration loads represent the structure's response to a imposed acceleration field — a manoeuvre load, a crash pulse, a vibration input. Gravity is a special case of acceleration load (9.81 m/s² downward). The critical input for inertia loads is the mass distribution, which depends on the material density and the modelled geometry. Non-structural mass — paint, sealant, fasteners, equipment, fuel — must be included, either as point masses, distributed mass, or non-structural mass density. Omitting non-structural mass underestimates inertia loads and can significantly affect the result for mass-critical structures.

• Acceleration load: F = m·a applied to every element — requires correct mass density
• Gravity: special case, 9.81 m/s² — always check the sign convention (which way is "down" in your model)
• Non-structural mass: paint, sealant, fasteners, equipment, fuel — include as point masses or distributed mass
• Centrifugal load: ω²r body force for rotating structures — requires axis of rotation and rotational speed

Inertia loads are only as accurate as the mass model. A model with correct stiffness but missing non-structural mass will produce the right deflections but the wrong inertia loads — and the wrong dynamic response.

Thermal Loads

A thermal load is a temperature field applied to the model. The temperature change produces thermal strain: ε_thermal = α·ΔT, where α is the coefficient of thermal expansion. If the structure is free to expand, the thermal strain produces deformation but no stress. If the structure is constrained — by supports, by attachment to a stiffer structure, or by a non-uniform temperature field that creates internal incompatibility — the thermal strain produces stress. The stress comes from the restraint, not from the temperature itself. A uniform temperature rise on a free structure produces zero stress; the same temperature rise on a constrained structure can produce significant thermal stress.

• Thermal strain: ε = α·ΔT — strain from temperature change
• Free expansion: no stress, only deformation
• Constrained expansion: stress from restraint — supports, attachments, or non-uniform temperature
• Temperature gradient: differential expansion within the structure — thermal stress even without external constraint

Imposed Displacement and Preload

An imposed displacement applies a known displacement to a surface or node, rather than a known force. The reaction force at the displaced boundary is the output, not the input. Imposed displacements are useful when the displacement is known (from a test, from a tolerance, from a press-fit interference) but the force is not. They are also useful for avoiding convergence problems — a displacement-controlled analysis converges more robustly than a force-controlled analysis in some non-linear problems, because the displacement is bounded. Preload is a special case: a bolt preload is applied as an imposed displacement (a bolt tension force) that clamps the joint. The preload must be applied and equilibrated before the external loads are applied, usually in a separate load step.

• Imposed displacement: known displacement, unknown reaction force — output is the reaction
• Press fit: interference between shaft and bore, applied as imposed displacement — resolves contact pressure
• Bolt preload: applied as bolt tension or imposed displacement, in a separate load step before external loads
• Displacement control: more robust convergence than force control for some non-linear problems

Remote Loads and Force Couples

A remote load applies a force or moment at a point that is not on the meshed geometry, distributing it to a selected surface through a rigid or kinematic connection. This is useful for applying a load at the centre of mass of an unmodelled component, or at the centre of a hole where a pin acts. A force couple — two equal and opposite forces separated by a distance — applies a pure moment to the structure. Force couples are useful for applying moments to shell models where rotational degrees of freedom exist, or to solid models where they do not (a moment cannot be applied directly to a solid node, which has only translational DOFs). The couple must be applied with a realistic lever arm; an arbitrarily short lever arm creates an artificial stress concentration.

• Remote load: force or moment at a remote point, distributed to a surface — for loads at unmodelled locations
• Force couple: equal and opposite forces separated by a distance — applies a pure moment
• Moment on solid: must be applied as a couple or via a remote point — solids have no rotational DOFs
• Lever arm: must be realistic — an artificially short lever arm creates a stress concentration

Coordinate Systems

Every load is applied in a coordinate system. The default is the global coordinate system, but many loads are more naturally applied in a local or cylindrical system. A pressure on a cylindrical surface is applied in a cylindrical system (radial, hoop, axial). A bearing load on a hole is applied in a cylindrical system. A load on a skewed bracket is applied in a local Cartesian system aligned with the bracket. The choice of coordinate system does not change the physics, but it makes the load definition simpler and less error-prone. Always confirm the coordinate system in which each load is applied, and check that the direction is correct — a load applied in the wrong direction is the same as no load at all.

• Global Cartesian: default — X, Y, Z
• Local Cartesian: user-defined origin and orientation — for skewed geometry
• Cylindrical: R, θ, Z — for cylindrical surfaces (holes, shafts, pipes)
• Spherical: R, θ, φ — for spherical surfaces (domes, ball joints)

A load applied in the wrong coordinate system, or in the right coordinate system with the wrong sign, is a silent error. The solver will not flag it. Always verify load directions by checking reaction forces and by visualising the load vectors before running the analysis.

Follower Loads

A follower load is a load that changes direction as the structure deforms — it "follows" the deformation. A pressure on a panel is a follower load: as the panel bends, the pressure remains normal to the deformed surface, not to the original surface. A follower load contributes to the stiffness matrix (it adds a "load stiffness" term), and this contribution can be stabilising or destabilising. A pressure on a panel is typically destabilising — it reduces the effective stiffness and can lower the buckling load. Most solvers allow follower loads to be turned on or off. For small deflection linear analysis, the effect is negligible and follower loads can be ignored. For large deflection non-linear analysis and for buckling analysis, follower loads must be included if the real load follows the deformation.

• Follower load: direction changes with deformation — pressure remains normal to the deformed surface
• Non-follower load: direction fixed in space — does not change with deformation
• Load stiffness: follower loads add a stiffness term that can be stabilising or destabilising
• Always on for: large deflection non-linear analysis, buckling with pressure loads
• Negligible for: small deflection linear analysis

Load Mapping from Other Analyses

Many FEA models receive loads from other analyses: pressure from CFD, temperature from a thermal analysis, loads from a multibody dynamics simulation, loads from a global structural model. Mapping these loads onto the FEA model is a critical step that is often under-appreciated. The loads must be transferred with the correct coordinate system, the correct units, the correct load case timing, and the correct spatial distribution. The mesh of the source analysis (CFD, thermal) is usually different from the mesh of the target analysis (structural), so the loads must be interpolated from one mesh to the other. This interpolation can introduce errors, particularly at edges, corners, and regions where the meshes are very different in resolution.

• CFD pressure: map pressure and shear stress from CFD mesh to structural mesh — check coordinate system and units
• Thermal field: map temperature from thermal model to structural model — different meshes require interpolation
• Multibody loads: map joint forces and moments from multibody model to structural model — check load case timing
• Global-local: map displacements from global model to sub-model boundary — see submodelling article

Load mapping is not a black box. Check the total force and moment on the structural model after mapping — they should match the source analysis. If they do not, the mapping has introduced an error, and the results are not trustworthy.

Load Application: A Practical Checklist

The way loads are applied defines the local stress field. The following checklist helps ensure that loads represent the real physics, not just the real magnitudes.

• Is the load distribution realistic? — Point load, distributed, bearing, pressure — match the real load transfer
• Are point loads kept away from regions of interest? — If not, replace with a distributed or bearing load
• Is the mass model complete? — Include non-structural mass for inertia loads
• Are coordinate systems and load directions verified? — Check reactions and visualise load vectors
• Are thermal loads applied with the correct reference temperature? — Stress comes from ΔT, not absolute T
• Are mapped loads checked for total force and moment? — Compare to source analysis
• Are follower loads included where needed? — Large deflection and buckling with pressure

Key takeaways

• How a load is applied matters as much as its magnitude — a point load and a distributed load with the same resultant produce completely different local stresses.
• Point loads create stress singularities — the stress increases without bound as the mesh is refined and never converges.
• Real loads are distributed over a finite area — bearing loads, contact pressure, fillet welds, adhesives — and the model should represent that distribution.
• Inertia loads are body forces applied to every element — they require mass density, not just stiffness, and they are sensitive to omitted non-structural mass.
• Thermal loads produce strain, not stress, until the structure is constrained — the stress comes from restraint, not from temperature itself.
• Loads from other analyses — CFD pressure, thermal fields, multibody loads — must be mapped carefully, with the right coordinate system, units, and load case timing.
• APPLY THE PHYSICS, NOT JUST THE NUMBER — a load applied in the wrong way produces the wrong stress, even if the magnitude is correct.