Modelling Bolts and Fasteners in Finite Element Analysis
The way a fastener is represented in FEA ranges from a rigid link to a fully three-dimensional solid model with thread contact. Each representation has different capabilities for preload, load recovery, local stress, joint compliance and contact fidelity — and a different computational cost. This article compares the common modelling approaches and provides guidance on selecting the right level of fidelity for the analysis objective.
The Spectrum of Fastener Representations
Fastener modelling in FEA spans a spectrum from the simplest one-dimensional idealisation to the most detailed three-dimensional solid representation. At one end, a rigid link connects the nodes on opposite sides of the joint with a constraint that allows no relative displacement — the fastener is infinitely stiff. At the other end, a solid bolt with threaded shank, nut, washers and contact at every interface captures the full mechanical behaviour — but at enormous computational cost. Between these extremes are beam fasteners, connector elements, spring elements and combinations thereof. The choice depends on what the analysis needs to capture: load distribution, fastener force, local bearing stress, bolt stress, or preload effects. No single representation is correct for all purposes — the engineer must select the level of fidelity that captures the relevant physics without excessive cost.
No single fastener representation is correct for all purposes. The representation must match the analysis objective: load distribution needs flexibility, fastener stress needs bending and axial behaviour, local bearing stress needs contact. Select the minimum fidelity that captures the relevant physics.
Rigid Links and Multi-Point Constraints
A rigid link (or multi-point constraint, MPC) connects the nodes on opposite sides of the joint with a rigid relationship — the nodes move together as if connected by an infinitely stiff pin. This representation is the simplest and cheapest: it enforces displacement compatibility across the joint and transfers load from one plate to the other. It does not capture fastener flexibility, fastener bending, fastener shear deformation or bearing deformation. The load distribution it produces is governed entirely by the plate stiffness and the rigid constraint — it overpredicts the load at the stiffest fastener locations and cannot capture the load-spreading effect of flexible fasteners. Rigid links are useful for preliminary sizing and for joints where the fastener flexibility is negligible compared to the plate flexibility (very stiff fasteners in compliant plates). They are not appropriate for final load-distribution analysis of multi-fastener joints.
Beam Fasteners
A beam fastener represents the fastener as a beam element connecting the nodes on opposite sides of the joint. The beam has a cross-section (the fastener shank area), a material (the fastener modulus) and a length (the grip length). The beam stiffness captures the fastener axial, shear and bending behaviour — it is not rigid, and it can deform under load. The beam fastener is a significant improvement over the rigid link because it captures the fastener flexibility, which is essential for accurate load distribution. The beam can be assigned the fastener shear stiffness, bending stiffness and axial stiffness. The load recovery is straightforward — the beam element forces and moments are directly available. The beam fastener does not capture the plate bearing deformation — the deformation of the plate material around the hole — unless the beam flexibility is adjusted to include a bearing compliance (the Huth approach: assign the beam a flexibility that includes both the fastener deformation and the plate bearing deformation).
Spring and CBUSH Elements
A spring element (or CBUSH in Nastran terminology) represents the fastener as a spring with specified stiffness in each of the six degrees of freedom (three translational, three rotational). The spring stiffness can be set to the fastener shear stiffness, axial stiffness and rotational stiffness independently. The CBUSH element is the standard way to implement Huth flexibility in FEA: the translational stiffness is set to the inverse of the Huth flexibility, and the element connects the nodes on opposite sides of the joint. The advantage of the spring approach is its simplicity and computational efficiency — a spring element has no bending, no stress field and no contact, so it is very cheap. The disadvantage is that it captures no local behaviour: no bearing stress at the hole, no fastener stress, no contact pressure. The load recovery is straightforward — the spring force is directly available. The CBUSH is the workhorse element for multi-fastener load distribution in production FEA of aerospace structures.
The CBUSH (or spring) element with Huth flexibility is the standard approach for multi-fastener load distribution in production FEA. It is simple, efficient and captures the essential compliance. It does not capture local stress — for that, a detailed submodel or solid fastener is needed.
Connector Elements
Connector elements are a higher-level abstraction available in modern FEA codes (Abaqus, Nastran, ANSYS). They are predefined fastener representations that combine spring behaviour with additional features: spacing rules, bearing options, failure criteria, preload capability and load visualisation. A connector element can represent a bolt with a specified preload, a specified flexibility and a failure force — all in a single element definition. The connector approach is more capable than a bare spring because it can include the fastener behaviour (flexibility, preload, failure) in a structured way, and the post-processing tools can extract the fastener forces, margins and utilisation directly. The connector element is the preferred approach for large-scale FEA of built-up structures with many fasteners, where the engineer needs both the load distribution and a structured way to assess fastener margins.
Pretension Elements and Preload Application
Preload in FEA can be applied in several ways. The pretension element (or bolt preload section) is a specialised element that applies a specified axial force to the bolt — it cuts the bolt and applies equal and opposite forces at the cut, then locks the cut to maintain the preload. This is the most physically accurate method: it applies the preload as a force in the bolt, and the bolt elongation and member compression are computed from the stiffness. The thermal shrink method applies a temperature change to the bolt that causes it to shrink by the amount corresponding to the preload elongation — the shrinkage creates the tension. The initial force method (for springs and connectors) simply assigns the spring or connector an initial force equal to the preload. Each method has limitations: the pretension element requires a bolt model with a defined section; the thermal method requires calculating the correct temperature change from the bolt stiffness; the initial force method is simple but does not capture the interaction between preload and external load unless the element stiffness is correctly assigned.
- Pretension element: applies a specified axial force — most physically accurate, requires a defined bolt section
- Thermal shrink: applies a temperature change that produces the correct bolt elongation — requires calculating the temperature from bolt stiffness
- Initial force: assigns the spring or connector an initial force — simplest, but must pair with correct stiffness to capture load sharing
- All methods require the bolt stiffness and member stiffness to be correctly modelled for the load-sharing behaviour to be captured
Solid Bolts and Detailed Thread Modelling
A solid bolt is a three-dimensional solid element representation of the fastener — shank, head, nut and optionally threads. The solid bolt captures the full mechanical behaviour: axial tension, shear, bending, bearing against the hole wall, contact under the head and nut, and stress concentrations at the thread root. The solid bolt with thread contact is the highest-fidelity representation: the threaded shank, the nut threads and the contact between them are modelled explicitly, and the stress concentration at the first engaged thread is captured. This level of detail is required for fastener stress analysis (fatigue initiation at the thread root), bolt failure analysis and bearing pressure distribution. The cost is enormous — a single solid bolt with threads can have tens of thousands of elements, and the contact at the thread interfaces is highly nonlinear. Solid bolts with thread contact are used for detailed submodel analysis of critical fasteners, not for global load distribution.
Washer Modelling and Bolt-Head Contact
The washer and the bolt head or nut distribute the clamp force over a finite area of the plate surface. In a solid bolt model, the washer can be modelled as a separate solid body with contact to the plate and to the bolt head — this captures the load distribution under the head and the effect of the washer on the bearing stress. The bolt-head contact — the contact between the bolt head (or nut) and the washer or plate surface — transfers the clamp force as a surface pressure. Without the washer, the bolt head bears directly on the plate, and the contact pressure is concentrated under the head edge — a potential source of surface damage and fretting. With the washer, the load is spread over a larger area, and the contact pressure is reduced. Modelling the washer and head contact is important for bearing stress under the head, for fretting analysis and for the accurate representation of the clamp force distribution in the compression cone.
Comparison of Modelling Approaches
The table below summarises the capabilities and costs of the common fastener modelling approaches. The engineer should select the approach that provides the necessary fidelity at the minimum cost — and should be prepared to use different approaches for different analysis phases (e.g., CBUSH for global load distribution, solid bolt for local stress verification of the critical fastener).
The common strategy is to use a low-fidelity model (CBUSH or connector) for global load distribution and a high-fidelity model (solid bolt) for local stress verification of the most critical fastener. This multi-fidelity approach captures the global behaviour efficiently and the local behaviour accurately.
| Approach | Computational Cost | Preload Capability | Load Recovery | Local Stress Fidelity | Joint Compliance | Contact Fidelity | Typical Use |
|---|---|---|---|---|---|---|---|
| Rigid link / MPC | Very low | None | Reaction force | None | None — rigid | None | Preliminary sizing only |
| Beam fastener | Low | Initial force or thermal | Element forces and moments | Fastener bending stress | Fastener stiffness only | None | Load distribution with bending |
| Spring / CBUSH | Very low | Initial force | Element force | None | Assigned flexibility (Huth) | None | Production multi-fastener load distribution |
| Connector element | Low | Built-in preload | Element forces, margins | None — bearing force at node | Assigned flexibility | None | Large built-up structures with fastener margins |
| Pretension + beam | Low–moderate | Pretension element — accurate | Element forces and moments | Fastener stress | Fastener stiffness | None | Preloaded joints with load sharing |
| Solid bolt (no threads) | High | Pretension or thermal | Section integration | Bolt stress, bearing stress | Full — contact and bearing | Head/nut/washer contact | Local stress, bearing pressure |
| Solid bolt with threads | Very high | Pretension or thermal | Section integration | Thread root stress concentration | Full | All contacts including threads | Critical fastener fatigue, failure analysis |
Friction, Bearing and Bolt Bending
Three behaviours that are often missed in fastener FEA deserve attention. Friction between the clamped plates transfers shear without fastener bearing — if the model does not include the contact between the plates with friction, this load transfer is missed and the fastener loads are overpredicted. Bearing — the fastener pressing against the hole wall — requires contact between the fastener and the hole surface; without it, the load transfer is through the nodes only, and the bearing stress is not captured. Bolt bending — the fastener bending as a beam — requires the fastener to have bending stiffness (beam or solid model); a spring element has no bending and cannot capture the bending stress that can be significant in single-shear joints with thick plates. The engineer should verify that the model includes the relevant behaviours: friction at the plate interface for friction-grip joints, contact at the hole for bearing stress, and bending stiffness for single-shear joints.
Three behaviours often missed in fastener FEA: friction between plates (missed without plate-to-plate contact), bearing at the hole wall (missed without fastener-to-hole contact), and bolt bending (missed with spring or rigid-link elements). Verify that the model includes the behaviours relevant to the analysis.
Key takeaways
- The fastener representation must match the analysis objective. A rigid link is adequate for load path but useless for bolt stress. A solid bolt with thread contact gives local stress but is impractical for a structure with hundreds of fasteners.
- Preload can be represented in FEA using pretension elements, thermal shrink, or initial force. The method must produce the correct clamp force without introducing artificial stress concentrations.
- Load recovery — extracting the fastener force, shear and moment from the FEA results — is straightforward for beam and connector elements but difficult for solid bolts, where the force must be integrated over a cross-section.
- Bolt bending is captured by beam and solid models but not by spring or rigid-link models. In single-shear joints with thick plates, bolt bending can contribute significantly to the fastener stress.