Finite element analysis (FEA) is a numerical method for predicting how a physical part behaves under load. The geometry is divided into a large number of small, simple shapes called elements, which meet at points called nodes. Simple equations describe the behaviour inside each element, the elements are assembled into one system for the whole part, and a computer solves that system. What comes out directly is how far every node moves. Strain, stress and the reaction forces at the supports are then calculated from those movements.
For real geometry, FEA reaches questions that handbook formulas cannot: whether a bracket yields at its worst-case load, how far a frame deflects, where a casting will crack first, or whether a housing is stiff enough to keep its natural frequency clear of the motor speed. It works alongside engineering judgement and physical testing, and lets a team compare designs and find weak points before anything is made, when a change costs least.
Why divide a part into elements
Classical formulas exist for simple shapes: a uniform beam, a thin cylinder, a flat plate with a round hole. A cast bracket with ribs, bosses, fillets and bolt holes has no such formula. FEA gets round this by breaking the shape into pieces that are each simple enough to describe on their own, then joining them so that neighbouring elements move together at their shared nodes.
For a static structural problem, the assembled system takes the form:
[K]{u} = {F}
Here K is the stiffness matrix of the whole model, u is the list of unknown nodal displacements and F is the list of loads applied at the nodes. Each node of a solid element can move in three directions, so a model with one million nodes has around three million unknowns. Modern solvers handle systems of that size routinely, and several design variants can be run side by side.
How an FEA model is built
Every model, however large, is made from the same five ingredients. The quality of the answer depends on each of them.
Geometry
The starting point is the CAD model, usually simplified. Logos, cosmetic chamfers and modelled threads add elements without changing the answer and are normally removed. Fillets in highly stressed regions stay, because they control the peak stress. Thin-walled parts can be represented by surfaces with a thickness (shells), long slender members by lines with a cross-section (beams), and a symmetric part by half or a quarter of its geometry.
Material
A linear static analysis needs only two elastic properties: Young’s modulus E, which sets stiffness, and Poisson’s ratio ν, which sets how much the material narrows as it stretches. Structural steel has E of about 200 to 210 GPa and ν of about 0.3; aluminium alloys have E of about 70 GPa and ν of about 0.33. Density is added for gravity and vibration work, the expansion coefficient for temperature loads, and a full stress-strain curve for anything that yields. Strength values, such as the 355 MPa minimum yield strength of S355 steel in thinner sections, are used to judge the results rather than to calculate them.
Loads
Forces, pressures, moments, bolt preload, gravity and other accelerations, temperatures and enforced displacements. Most products have more than one load case: lifting, transport, normal operation, an overload or abuse condition. The load is frequently the least certain input. A precise model with a guessed load gives a precise answer to the wrong question, so it pays to establish what actually acts on the part, where, and in which direction.
Constraints
Constraints, or boundary conditions, describe how the part is held: fixed faces, pins, sliding supports, bolted joints and contact with neighbouring parts. They affect the results as much as the loads do. Fully fixing a face that in reality can flex or slide makes the model stiffer than the real part and can put stress where none exists. Leaving the part free to move as a rigid body means there is no static solution at all.
Elements and mesh
The mesh is the collection of elements. Second-order elements, which have mid-side nodes and can take a curved shape, represent stress gradients far better than first-order elements of the same size; first-order tetrahedra in particular are too stiff in bending. Elements are made smaller where stress changes quickly, around holes, fillets and contact edges, and larger elsewhere to keep the model to a sensible size.
| Element type | Suited to | Typical examples |
|---|---|---|
| Solid (tetrahedral or hexahedral) | Three-dimensional parts where stress varies through the thickness | Castings, forgings, machined blocks, levers |
| Shell | Walls that are thin compared with their other dimensions | Sheet metal enclosures, tanks, vehicle panels |
| Beam | Long, slender members described by their cross-section | Frames, trusses, racking, tubular structures |
| Spring, mass and connector | Bolts, bearings, mounts or heavy items that need no detailed model | A motor carried on a frame, anti-vibration mounts |
What the results mean
Displacement
Displacement is the primary result: how far, and in which direction, each point moves. It is often the deciding criterion in its own right. A machine frame may be strong enough but deflect too much to hold alignment; a cover may survive a load but touch the circuit board behind it. Deformed shape plots are usually exaggerated by a scale factor so the pattern can be seen; the numbers give the real movement.
Strain
Strain is deformation relative to original size, ε = ΔL / L, and has no units. Elastic strains in metals are small: S355 steel reaches yield at a strain of about 0.0017, which is 355 MPa divided by 210 GPa. Strain becomes the main result for plastics, elastomers and any analysis in which the material yields, because their limits are then better expressed as a strain than a stress.
Stress
Stress is internal force per unit area, reported in MPa (1 MPa = 1 N/mm²). At any point there are six stress components, three direct and three shear, so results are normally shown as a single equivalent value. For ductile metals that is the von Mises stress, compared with yield strength; for brittle materials such as cast iron and glass, the maximum principal stress is more meaningful. Our guide to von Mises stress covers the difference. The ratio of strength to calculated stress gives the factor of safety at each point.
Red on a contour plot means only the top of the colour scale. Whether it is a problem depends on the value against the limit, the material and the type of load. Reaction forces at the supports and the forces in bolts and pins are also available, and are often what you need to size fasteners, bearings and foundations.
Types of FEA and the questions they answer
| Analysis | Question it answers | Example |
|---|---|---|
| Linear static | Stress and deflection under steady loads, below yield | A lifting lug at its rated load |
| Non-linear static | Behaviour beyond yield, large deflection, contact that opens or slides | A snap-fit clip during assembly |
| Modal | Natural frequencies and mode shapes | A pump skid frame near running speed |
| Harmonic and random vibration | Response to cyclic or broadband shaking | Electronics on a vehicle-mounted rack |
| Fatigue | Life under repeated load | A welded trailer drawbar |
| Thermal stress | Stress caused by temperature change and gradients | A flange on a hot exhaust |
| Drop and impact | Response to short, violent events | A handheld device dropped onto concrete |
Most structural questions start as stress analysis. When yield, large movement or changing contact matters, non-linear analysis takes over. When the load repeats, fatigue analysis decides the life, and where anything rotates or vibrates, vibration analysis shows where the resonances lie.
Where FEA is most useful
- New designs without precedent, where there is no earlier product to learn from.
- Before committing to tooling for castings, mouldings or forgings, when a change still costs a CAD edit rather than a new tool.
- Weight and cost reduction: removing material where stress is low, or replacing steel with aluminium, or a fabrication with a casting.
- Understanding a failure in service: reproducing the stress pattern that cracked a part, then trying the fix in the model before it is made.
- Fewer prototypes: screening options so that physical tests are spent on the strongest candidate.
What FEA cannot tell you
FEA solves the model it is given. Its limits are mostly the limits of the inputs and assumptions.
- Wrong inputs give precise-looking wrong answers. An underestimated load, an over-stiff support or the wrong material grade will not be flagged by the software.
- Linear analysis stops at yield. A linear result of 450 MPa in S355 steel does not mean 450 MPa exists in the part. It means the material has yielded and the load has redistributed, which only a non-linear analysis can describe.
- Sharp corners need their real radius. A perfectly sharp internal corner has, in theory, infinite elastic stress. Real parts have a radius, and the model needs it to give a meaningful peak.
- Manufacturing is not in the model unless it is put there. Weld residual stress, casting porosity, surface finish, heat-affected zones and material variability all affect real strength.
- Some failures need their own analysis. A static stress result does not predict buckling, fatigue life or brittle fracture; each needs a dedicated study.
- Physical tests keep their place. A product that needs type approval still needs the physical evidence its standard asks for.
When to bring in a specialist
FEA software is widely available. Most of the value lies in the judgement around it: what to model, which loads govern and what the results mean for the design. A SixGate™ FEA study ends in practical changes to geometry, material or process, with design variants compared side by side where the decision calls for it and results reported against the code or standard you specify. Analysis sits inside the detail design and simulation stage, so the engineers who find the weak point can redesign the part, draw it for manufacture and see it into production. The FEA and structural mechanics page sets out the analyses on offer.