4. Preload modeling for bolts

Every bolted joint in a nonlinear contact simulation exists to do one thing: hold clamped members together with a controlled clamping force. That force is the preload, and how you introduce it into the finite element model determines whether your contact pressures, gap states, and load paths are physically meaningful or merely plausible-looking numbers. This chapter covers the four mechanisms you will use in practice — pretension elements, thermal preload, initial strain, and the distinction between force-controlled and displacement-controlled tightening — and shows how each maps onto the solver's contact formulation.

Why Preload Is Not Just an Initial Condition

Preload is a self-equilibrated internal stress state. The bolt stretches, the clamped members compress, and the two forces balance. In a nonlinear contact analysis this matters because the preload state defines the initial gap/penetration status of every contact interface. If you apply preload as a simple nodal force on the bolt head, you will get the right bolt tension but the wrong member compression distribution, and the contact stiffness at the faying surface will be wrong from increment one.

The three standard modeling routes are:

  • Pretension element / pretension section — a dedicated 1-D element or a cut plane through the bolt shank that enforces a target axial force or adjustment length.
  • Thermal preload — a fictitious temperature drop in the bolt (or a temperature rise in the members) that produces the same axial contraction as tightening.
  • Initial strain / interference — a prescribed initial strain in the bolt shank, or a geometric interference between shank and hole, that generates the clamping force.

All three are legitimate; the choice depends on whether you need a force target, a displacement target, or a stress-free reference state that survives multiple load steps.

Pretension Elements and Pretension Sections

A pretension element is a two-node axial element inserted along the bolt axis. You specify either a preload force or an adjustment length. The solver then solves for the nodal displacements that produce that force, and the resulting displacements are applied to the surrounding mesh as boundary conditions. In Abaqus this is the *PRE-TENSION SECTION; in ANSYS it is PRETS179; in Nastran it is the BOLT entry with a PSHELL/PBAR shank.

The critical implementation detail is the cut plane. The pretension section must cut the bolt shank cleanly, and the two cut faces must be tied to the pretension node. If the cut plane passes through a fillet or a thread root, the local stress concentration will be wrong. Place the cut in a straight, uniform shank region, typically one to two diameters below the head.

*PRE-TENSION SECTION, ELSET=BOLT_SHANK, NODE=1001
1001, 0.0, 0.0, 0.0
*CLOAD
1001, 1, 25000.0   ! target preload 25 kN

After the preload step, you must lock the pretension node (fix its axial DOF) so the bolt behaves as a structural member in subsequent load steps. Forgetting this lock is the single most common cause of "the bolt unloads as soon as I apply external load."

Thermal Preload

Thermal preload exploits the fact that a constrained thermal contraction is mechanically equivalent to a tightening displacement. If the bolt is restrained axially by the clamped members, a temperature drop ΔT produces an axial force:

F = E · A · α · ΔT

where E is Young's modulus, A the shank cross-section, and α the coefficient of thermal expansion. For a steel bolt with E = 210 GPa, A = 245 mm² (M20), and α = 1.2 × 10⁻⁵ /°C, a ΔT of −100 °C gives approximately 61.7 kN — far more than a typical M20 preload. In practice you scale ΔT to hit the target force, and you must assign a zero-expansion material to the clamped members (or a matched expansion that cancels) so only the bolt contracts.

Thermal preload is convenient because it works in any solver that supports thermal expansion, but it is a displacement-controlled mechanism. If the joint opens, the bolt force drops; if the members creep, the force redistributes. Do not use it when you need a guaranteed constant force under large external loading.

Initial Strain and Interference

Initial strain is the most direct route: prescribe a negative axial strain in the bolt shank elements. The equivalent preload is F = E · A · ε₀. This is attractive in explicit solvers where pretension elements are unavailable, but it requires that the shank mesh be aligned with the bolt axis and that the strain be applied before any contact is established. A common alternative is geometric interference: model the shank slightly oversized relative to the hole, or the members slightly thinner than the bolt grip length, and let the contact solver resolve the interference in the first step. This is physically intuitive but numerically stiff — expect to use contact stabilization or a ramped interference in the first increment.

Force-Controlled vs. Displacement-Controlled Tightening

This distinction is not academic. It determines the stiffness of the system you are solving and the convergence behavior you will see.

Aspect Force-controlled Displacement-controlled
Input Target axial force (N) Adjustment length or ΔT (mm or °C)
Physical analogue Torque wrench to a torque spec Turn-of-nut / stretch measurement
Joint stiffness effect Force is independent of member stiffness Force depends on member and bolt stiffness
Convergence Usually easier; force is a natural BC Can be stiff if members are soft
Best for Specified preload, torque-controlled joints Stretch-controlled joints, thermal analogues

In a force-controlled analysis, the solver adjusts the bolt length until the reaction at the pretension node equals the target. The clamped members see whatever compression that force produces. In a displacement-controlled analysis, you prescribe the bolt shortening and read the resulting force. The two give identical results for a linear joint, but diverge once contact nonlinearity, plasticity, or gasket creep enters.

Worked Example: M20 Bolt Through Two Steel Plates

Consider two 20 mm steel plates clamped by an M20 × 2.5 bolt with a 245 mm² tensile stress area. Target preload is 70% of proof load, approximately 110 kN. The bolt grip length is 40 mm. Using a pretension section at mid-grip:

  1. Mesh the bolt shank with hex elements, cut at mid-grip, and define the pretension node.
  2. Apply a *PRE-TENSION SECTION with a target force of 110 kN in Step 1.
  3. Lock the pretension node axial DOF at the end of Step 1.
  4. Apply external tensile load in Step 2 and monitor bolt force and contact pressure.

Expected observable results: bolt axial force stays near 110 kN until the external load exceeds the clamp force, at which point the joint opens and the bolt force rises. Contact pressure at the faying surface should be roughly uniform under the washer footprint and drop to zero outside it. If you see contact pressure concentrated at the hole edge, your mesh is too coarse or the washer is not modeled.

Always run a preload-only step first and check that the bolt force matches the target and that the member compression is symmetric. If the force is off by more than 2%, check the pretension section orientation and the shank cross-section area.

Choosing the Right Method

Use pretension elements when your solver supports them and you need a force target — this is the default for implicit structural analysis. Use thermal preload when you are working in a solver without pretension elements, or when you want to combine preload with a real thermal load case. Use initial strain for explicit dynamics or when the bolt is modeled with solid elements and no dedicated pretension feature exists. Use displacement-controlled tightening when the physical process is turn-of-nut or stretch-controlled, or when force-controlled convergence stalls due to contact chatter.

Preload Modeling Routes and Their Mechanical Equivalence Physical Joint Head Shank Plate 1 (20 mm) Plate 2 (20 mm) Nut F_preload F_preload compression Modeling Routes 1. Pretension Element Cut plane + pretension node Target force or adjustment Lock node after Step 1 2. Thermal Preload ΔT on bolt only F = E·A·α·ΔT Members: α = 0 3. Initial Strain Prescribed ε₀ in shank F = E·A·ε₀ Or geometric interference Control Mode Force-Controlled Input: target force Solver adjusts length Force independent of member stiffness Easier convergence Displacement-Controlled Input: ΔL or ΔT Solver reads force Force depends on bolt + member stiffness Stiffer, may stall All three routes produce the same self-equilibrated preload state; the choice depends on solver capability, required control mode, and whether thermal or strain loads are already present.

The diagram above summarizes the decision space. The physical joint on the left is what you are trying to represent; the middle column shows the three numerical routes; the right column shows how each route maps onto force- or displacement-controlled tightening. In practice you will pick one route per bolt group and stay consistent across all load steps, because mixing routes within a single joint can produce inconsistent initial contact states.

Practical Checks Before You Run

  • Verify the shank cross-section area used in the preload calculation matches the actual tensile stress area, not the nominal diameter area.
  • Confirm the pretension node is locked after the preload step; otherwise the bolt will relax under external load.
  • Check that the contact interfaces under the head and nut are initialized with the correct gap or interference.
  • For thermal preload, confirm the clamped members have zero thermal expansion, or that their expansion is accounted for in the target ΔT.
  • Run a preload-only step and compare the bolt reaction force to the target; a mismatch above 2% usually indicates a modeling error, not a solver tolerance issue.

With the preload state correctly established, the subsequent nonlinear contact solution will reflect the true stiffness of the clamped assembly. The next chapter builds on this foundation by examining how frictional contact at the faying surface interacts with the preload state under external shear and tension.

← Previous 📖 Contents Next →