Finite element analysis has long left the research lab. Solvers sit at every design group, licenses for Ansys, Femap, and a built-in Nastran live on laptops, and preprocessors hide most of the math behind the interface. The result is a familiar pattern: an engineer builds a model, runs the solve, and gets a clean set of stress contours. The contours do not prove that the structure passes a code check. Between the solver run and a signed Eurocode 3 or ASME VIII report sits a set of techniques without which FEA stays a numerical decoration.Drawing on what is finite element analysis, the following sections walk through the techniques that shape result quality from preprocessing to the moment FEA output gets compared against code requirements
Element type selection
The choice of element (beam, shell, or solid) sets the accuracy ceiling of the model before the mesh even exists. A beam element describes a truss or a frame through four degrees of freedom per node and runs fast. It does not capture the stress distribution across an I-section web. Shell elements suit thin-walled structures: a ship hull, a tank wall, or a connection plate. Solids are needed wherever the stress state is fully three-dimensional, such as thick welds, forged components or contact with curved geometry.
Hexahedra (bricks) reach more accurate results at lower element counts than tetrahedra. On the same geometry, a hex mesh hits convergence at the second or third refinement level, while a tet model needs five or six. Element choice is the first decision that no amount of refinement or extra nodes can undo.
Mesh and convergence
Mesh density controls how closely the discrete solution approaches the continuous problem. Coarse meshes underpredict peak stresses. On a typical structural detail, a 10 mm element gives a maximum of 85 MPa, while a converged 1.5 mm mesh returns 102 MPa. The gap is roughly 17%. At a utilization of 0.95, that difference flips a code check from a fail to a formal pass.
Convergence is demonstrated across at least three refinement levels. NAFEMS places the peak stress variation between successive refinements within 2-5%. DNVGL-RP-F112 tightens the threshold to 3% when the element size is halved in linear analysis and 5% on total strain energy for nonlinear runs. Displacements converge faster than stresses. Displacements stay the primary unknowns of the system. Stresses are derived by differentiating the displacement field.
A separate trap sits at singularities. An internal corner without a radius produces a stress that climbs without bound as the mesh refines. This is a mathematical consequence of the chosen idealization, with no physical material failure behind it. Singular points are handled either by averaging the stress and applying section linearization or by removing them from the model with a geometric fillet.
Boundary conditions
Boundary conditions outweigh every other source of FEA error in frequency, more often than meshing problems, more often than solver issues. An over-constrained model looks stiffer than the real structure. An under-constrained one drifts as a rigid body and refuses to converge. A point load applied directly to a shell node generates a local stress spike that mesh refinement only amplifies.
Symmetry is used to cut the model size. Symmetric boundary conditions require symmetric loading and symmetric material. Without that, the result loses meaning. Contact pairs are defined with explicit reference to surface normals and friction. Contact stiffness is set so that penetration stays a small fraction of the element thickness.
Linear or nonlinear analysis
Linear static analysis remains the default for structures under small deformations, linear material behavior, and constant boundary conditions. It covers most buildings and assemblies. Once strains exceed roughly 5%, the material crosses yield, or the structure loses stability and enters a post-buckling regime, or the linear formulation stops being valid.
Eigenvalue buckling returns a critical load. It says nothing about what happens beyond it: whether the system collapses, redistributes load, or stabilizes in a deformed shape. For an eccentrically loaded column, linear analysis underpredicts deflections by orders of magnitude compared to a full nonlinear run. Offshore structures and stamping equipment move to nonlinear FEA through Riks or arc-length methods with NLGEOM active. Stabilization energy ALLSD is held below 5% of strain energy ALLSE. Kinetic energy ALLKE for quasi-static explicit runs stays under 5-10% of internal energy ALLIE.
Load combinations
EN 1990 writes the ULS combination as 1.35·G_k + 1.5·Q_k,1 + 1.5·ψ₀·Q_k,2. The formula is short. The final count of combinations for a mid-complexity building passes 50 routinely, while an offshore module under wave, wind, and current reaches several hundred. The second-generation Eurocode adds a consequence factor kF and expands the consequence class table from three to five. Both shifts increase the number of combinations and the magnitude of their summed effects.
An engineer who hand-picks a handful of “representative” cases runs the risk of missing the governing one. Automated extraction of governing loads from the full set closes that gap once the combination count climbs past 30-50.
Stress interpretation
A von Mises contour on screen is not the stress that compares against the code allowable. ASME VIII Div. 2 Part 5 splits stresses into five categories: general membrane Pm, local membrane PL, bending Pb, secondary Q, and peak F. Each carries its own allowable level. Section linearization separates the through-thickness stress distribution into membrane and bending components through integration along the classification line.
The linearization path runs through the zone of interest and is checked in parallel for contact with a singularity. If it hits one, the linearization result becomes mesh-size dependent and cannot serve as a code-compliant value. Dimensionless utilization (demand/resistance) must stay at or below unity. The check runs on properly classified stresses. A contour maximum does not qualify.
Fatigue analysis
In industries built around cyclic loading (lifting equipment, offshore platforms, bridge trusses), fatigue failure accounts for a large share of in-service failures. The S-N approach and damage accumulation through the Palmgren-Miner rule D = Σ(n_i / N_i) form the backbone of the check. The failure criterion formally triggers at D ≥ 1.0. In design practice, a margin is kept, and the working target lands closer to D ≤ 0.5-0.7.
The hot spot stress method used by DNV-RP-C203 for welded offshore details calls for a fine mesh at the weld toe and a linear extrapolation from two reference points at 0.5t and 1.5t from the toe. A mesh coarser than that spacing makes the extrapolation invalid. Fatigue technique drives mesh requirements locally. There is no universal “one mesh for the whole model” rule in FEA.
From stress to code verification
FEA delivers stresses, displacements, and reactions. The code delivers allowables and interaction formulas. Between these two sets sits a formal translation step. EN 1993-1-1 covers interaction equations for members under combined loading. EN 1993-1-5 supplies plate stability formulas through the effective width method. EN 1993-1-9:2025 carries the updated S-N curves. AISC 360-22 closes the same set of checks for the US market through equations H1-1a and H1-1b.
NAFEMS published the 2025 reference R0139 specifically on the link between FEA and code verification. It states the risk of double-counting effects directly: safety factors already embedded in the SCF coming out of FEA, then reapplied at the code stage. For structures under class society scrutiny, such as DNV, Bureau Veritas, or ABS, this transition is documented in a dedicated section of the report.
Code verification closes the loop. The model is solved, the mesh has converged, the boundary conditions hold up physically, the load envelope is covered through combinations, the stresses are interpreted, and fatigue is checked. Without this final step, FEA remains a numerical experiment. With it, the analysis becomes engineering evidence that an audit or a certification process can stand on.
