Finite Element Analysis You Can Defend in a Review

The failure mode

FEA never refuses. Apply nonsensical restraints, omit a load, use the wrong material, and you still get a smooth stress plot with a maximum value and a comforting colour scale.

Because the output always looks like an answer, the discipline has to come from outside the software. These are the checks that separate a defensible analysis from a rendered guess.

Boundary conditions cause most errors

Not meshing. Not element choice. Restraints.

Over-constraint is the most common and most damaging. Fixing a face in all six degrees of freedom when the real joint permits rotation introduces artificial stiffness and a spurious stress concentration at the restraint. Structures are frequently reported as failing at exactly the point where the analyst clamped them.

Under-constraint produces rigid body motion, which at least announces itself as a singular stiffness matrix or wildly implausible displacements.

Two practical habits help. Ask what physically holds the part, and represent that, not what is convenient to select. And check the reaction forces: they must sum to the applied load. If they do not, load is leaking into a restraint you did not intend.

Sanity-check with hand calculations

Before trusting any FE result, produce an independent estimate. Beam bending, a simple axial stress, a thin-wall pressure formula — anything giving a number of the right order.

If the FE result and the hand calculation differ by a factor of three, one is wrong, and it is worth knowing which before the design review rather than during it. This single practice catches unit errors, wrong material assignment, mis-scaled geometry and misapplied loads more reliably than any other check.

Without a prior expectation, every result looks plausible.

Convergence applies here too

As with CFD, results depend on mesh density and must be shown not to. Refine and re-run; the quantity of interest should stabilise.

The critical caveat is singularities. At a sharp re-entrant corner, the theoretical stress is infinite. Refining the mesh there produces an ever-increasing peak stress that never converges — the model is faithfully reproducing an artefact of an idealised geometry.

The response is not to refine further. It is to either model the real fillet radius, or to evaluate stress a small distance away from the singularity, or to use a fatigue method that accounts for the notch explicitly. Reporting the peak stress at a sharp corner as if it were physical is a common and serious error.

Element choice matters

• Linear tetrahedra are prone to shear locking and are overly stiff in bending. Avoid them for stress results in bending-dominated parts.
• Quadratic elements capture bending far better for the same element count and are the sensible default for stress analysis.
• Shells are appropriate where thickness is much smaller than the other dimensions, and vastly cheaper than solids for thin structure.
• Aspect ratio and distortion degrade accuracy; check element quality metrics rather than assuming the mesher behaved.

Know which assumptions you have accepted

A default static linear analysis assumes small displacements, linear elastic material, and no contact changes. Each may be wrong:

• Large displacement — a slender component deflecting significantly needs geometric nonlinearity, or stiffness will be badly overestimated
• Plasticity — if predicted stress exceeds yield, the linear result is not describing reality
• Contact — surfaces that separate, slide or bear on each other are nonlinear by nature
• Buckling — a stress result says nothing about stability; run an eigenvalue buckling analysis for slender members in compression

If the linear solution predicts stress above yield anywhere other than a known singularity, the linear solution is invalid at that location and must be flagged rather than reported.

What a defensible report contains

Geometry and any simplifications made, material properties with their source, loads and their derivation, boundary conditions with the physical justification, element type and mesh convergence evidence, reaction force check, the hand calculation comparison, and margins stated against a defined allowable.

A stress plot on its own is not an analysis. It is an illustration of one.