3. Structural linear static analysis review
Linear static analysis remains the workhorse of body-in-white (BIW) structural verification. Before any modal, crash, or fatigue study is trusted, the linear static model must be defensible: the load cases must represent real duty cycles, the constraints must not introduce artificial stiffness, and the reported stress must be mesh-converged rather than a numerical artifact. This section covers how to review those four pillars — load cases, constraints, stress singularities, and acceptance criteria — for BIW components such as rails, shock towers, crossmembers, and closures.
Load Case Definition and Review
A load case is only meaningful when its magnitude, direction, application point, and coordinate convention are all traceable to a source. For BIW linear static work, typical load cases include:
- Global bending and torsion — a 1 g vertical load or a prescribed twist angle applied at the suspension pickup points, used to check body stiffness and panel stress.
- Corner / pothole loads — a single-wheel vertical force (often 2–3 g) applied at one wheel center, producing a combined bending–torsion response.
- Braking and cornering — longitudinal or lateral inertia loads reacted at the suspension and powertrain mounts.
- Component-level loads — seat belt anchorage (SBA) pull, door slam, hood latch, or hinge loads, each with a regulatory or internal target.
During review, confirm that the load is applied through a realistic interface. A point load on a single node of a thin rail will produce a local stress spike that has no physical meaning. Instead, distribute the load over a rigid element (RBE2/RBE3) or a patch of nodes representing the bushing or bracket footprint. Verify the sign convention: if the model uses Z-up and the load case specifies a downward force, the applied value must be negative in Z. A frequent review finding is a load applied in the wrong global axis because the CAD and solver coordinate systems were not reconciled.
Constraint Strategy and Over-Constraint Detection
Constraints in a linear static BIW model serve two purposes: to react the applied load and to prevent rigid body motion. The most common error is over-constraining the model by fixing regions that should be free to deform. For example, fully constraining all nodes of a shock tower base will artificially stiffen the tower and under-predict stress in the rail. A better approach is to constrain only the minimum degrees of freedom needed for stability, using springs or bushings with realistic stiffness where the component attaches to the rest of the vehicle.
Review the constraint set against the following checks:
- Is the model statically determinate or is it redundantly constrained? Use the solver's constraint reaction report to identify unexpected forces.
- Are constraints applied at the correct location — e.g., at the bushing center rather than the bracket bolt hole?
- Do the constrained DOFs match the physical attachment? A bolted joint may transfer all three translations and rotations, while a bushing may only transfer selected directions.
- Is the constraint stiffness realistic? A rigid constraint (SPC) is acceptable only when the attached structure is much stiffer than the component being analyzed.
A practical technique is to run a free-free modal check first. If the first six modes are near zero, the model is unconstrained. Then apply the intended constraints and verify that the reaction forces sum to the applied load. A mismatch indicates either a missing constraint or an unintended load path.
Stress Singularities: Identification and Treatment
Stress singularities are non-physical stress concentrations that occur at re-entrant corners, point loads, and abrupt geometry changes. In linear static FEA, the stress at a singularity increases without bound as the mesh is refined. Reporting such a value as a design stress is a classic review failure.
Common singularity locations in BIW models include:
- Sharp interior corners of stamped ribs or cutouts.
- Nodes where a point load or SPC is applied directly.
- Edges of rigid elements (RBE2) connected to shell meshes.
- Intersections between shell and solid elements without proper transition.
To distinguish a singularity from a real hot spot, perform a mesh convergence study. Refine the mesh locally by a factor of two and re-run. If the peak stress doubles or grows unbounded, it is a singularity. If it converges to a stable value, it is a real stress concentration that can be compared against allowables. For singularities, either ignore the peak value and use a stress averaged over a defined region (e.g., a 5 mm radius), or remove the singularity by adding a small fillet, distributing the load, or using a more realistic constraint.
Acceptance Criteria and Sign-Off
Acceptance criteria for BIW linear static analysis are typically expressed as either stress limits or stiffness targets. Stress limits are compared against material yield with a safety factor, while stiffness targets are compared against a global or local displacement requirement.
| Criteria Type | Typical Metric | Example Target | Review Action |
|---|---|---|---|
| Material yield | Von Mises stress | ≤ 0.8 × yield for steel | Check mesh convergence; exclude singularities |
| Global bending stiffness | Max vertical deflection | ≤ 1.5 mm at seat rail | Verify load and constraint locations |
| Global torsion stiffness | Twist angle per unit torque | ≥ 10,000 Nm/deg | Check reaction torque balance |
| Local panel stiffness | Deflection under palm load | ≤ 0.5 mm | Confirm load patch size and boundary |
When reviewing a report, confirm that the acceptance criteria are stated with the same units and coordinate system as the results. A common pitfall is comparing a stress in MPa against a yield in ksi. Also verify that the safety factor is applied consistently: some teams apply it to the load, others to the allowable. The sign-off should document which convention was used.
For a typical BIW component such as a front shock tower, a complete review might proceed as follows. The load case is a 3 g vertical load applied at the wheel center, distributed over a 50 mm diameter patch on the tower top. Constraints are applied at the tower-to-rail interface using bushings with 10,000 N/mm stiffness. The mesh is refined to 3 mm shells with a 5 mm fillet at the tower-to-rail junction. The peak stress away from the singularity is 180 MPa, below the 250 MPa yield with a 1.4 safety factor. The global deflection at the wheel center is 1.2 mm, within the 1.5 mm target. The reaction forces sum to the applied load within 0.5%. The analysis is signed off with the note that the stress at the rigid element connection is a singularity and is excluded from the margin assessment.
The review process is not a one-time check but an iterative dialogue between the analyst and the design engineer. Each load case, constraint, and stress result should be traceable to a physical assumption. When a singularity is identified, the correct response is to document it and exclude it from the margin, not to hide it. When a constraint is over-stiff, the fix is to replace it with a realistic bushing or spring. When a load case is ambiguous, the fix is to return to the source and clarify the duty cycle. By applying these four pillars consistently, the linear static analysis becomes a reliable basis for BIW structural sign-off.