Nonlinear Contact Analysis of Bolted Joints
Nonlinear Contact Analysis of Bolted Joints: Theoretical Foundations
Nonlinearity of Bolted Joints
Professor, how does the nonlinear contact analysis of bolted joints differ from the bolted assemblies we learned in linear-static analysis?
Linear-static bolt analysis assumes no separation (linear). Nonlinear contact analysis tracks separation, sliding, and variation in clamping force.
Nonlinear Effects
| Nonlinear Effect | Description |
|---|---|
| Separation of clamped surfaces | Clamped surfaces open due to insufficient preload |
| Frictional sliding | Clamped surfaces slide under lateral load |
| Variation in bolt axial force | Bolt axial force changes under external load (Φ in VDI 2230) |
| Gasket nonlinearity | Compression-unloading hysteresis of gaskets |
| Preload relaxation | Preload decreases due to vibration or creep |
To track all of these with FEM, a nonlinear analysis with contact and preload is necessary, right?
Build a complete model with solid elements for bolt + clamped parts + contact (with friction) + preload, and solve it with nonlinear static analysis (Newton-Raphson).
Summary
Key Points:
- Track separation, sliding, and axial force variation — Not possible with linear analysis
- Combined nonlinearity of contact + friction + preload — Difficult to converge
- Compare with VDI 2230 hand calculations — Verification of FEM
- Especially important for flanges with gaskets — Gasket nonlinearity
VDI 2230 Guideline 1977
The bolted joint design standard VDI 2230 was established in 1977 in West Germany (at the time) and is one of the first industrial standards to systematically organize the relationship between clamping force, external load, and tightening allowance using a linear spring model. The basic concept treats the elastic compliance of the fastener and clamped parts as springs in series and defines the load introduction factor. The current 2014 edition officially recognizes calculation of this factor using FEM.
Computational Methods for Nonlinear Contact Analysis of Bolted Joints
FEM Settings
Typical settings in Abaqus:
```
*STEP, NLGEOM=YES
*STATIC
*BOLT LOAD
bolt_section, bolt_mid, 50000. $ Preload 50kN
*CONTACT PAIR
flange_top, flange_bottom $ Clamped surfaces
*FRICTION
0.15 $ Friction coefficient
*END STEP
*STEP, NLGEOM=YES
*STATIC
*BOLT LOAD, OP=FIX $ Fix preload
*CLOAD
...
*END STEP
```
Step 1 for preload, Step 2 for external load. OP=FIX locks the preload.
Summary
Implementation of Preload Elements
In FEM implementation of bolt tightening, the preload element method, which defines a cut section (bolt cut section) on the bolt shaft cross-section and applies an equivalent axial force there, is standard. In ABAQUS, this is implemented with the PRETENSION SECTION keyword, and a two-step process is recommended: applying the tightening load in the first analysis step, then adding external loads in the second step. This method is also adopted in MSC Nastran's BOLT element (V2010~).
Nonlinear Contact Analysis of Bolted Joints in Practice
Practical Application of Nonlinear Bolted Joints
Important for pressure vessel flanges (with gaskets), engine cylinder heads, and structural fasteners.
Practical Checklist
Sealing Evaluation of Flange Joints
In pipeline flanges for petrochemical plants, the uniformity of gasket contact pressure directly affects sealing performance. In an analysis case published by Mitsubishi Heavy Industries in 2012, non-uniform tightening of 24 bolts (±15% torque variation) was reproduced using ANSYS Workbench nonlinear contact, identifying locations where gasket pressure locally fell below the required minimum pressure (20MPa). Optimizing bolt arrangement improved sealing test pass rates from 78% to 96%.