lilernoEngineeringOpening Lilerno
Chapter 22 · Guided self-study
Intro + external course studyExplain why a plausible simulation picture is not proof of a correct model.
Build the idea
An original introduction, worked example and practice, followed by a curated reading sequence. The external courses supply deeper teaching and problem sets.
This guide is an orientation, not a complete university module. Practical work needs suitable facilities, safety review and supervision.
Start with these prerequisites
Shared science foundations
Simulation is another calculation to interrogate. A colourful contour is not evidence until the model, discretization and comparison are documented.
Module lens
A model is credible when assumptions, boundary conditions and a known reference are compared explicitly.
Check units, constraints, applied loads and conservation. Refine the mesh and observe a defined quantity, not just the image. A stress singularity may prevent pointwise peak stress from converging.
Verification asks whether the equations were solved appropriately; validation asks whether the equations represent the physical situation for the intended purpose. Agreement with another solver is not experimental validation.
See the relationship
Change one quantity, watch the graph respond, then explain the result in your own words.
Predict → change → explain
Does a finer mesh always change the answer?
Axes: Position along bar (m) → Displacement (mm). Bounds may rescale when inputs change.
End extension = 0.005 mm for any displayed mesh. A linear field needs no refinement here; more complex models can behave differently.
Uniform linear elastic bar: L = 1 m, A = 100 mm², E = 200 GPa, fixed left end and axial end force. Linear elements reproduce this linear displacement exactly; this is an analytical benchmark, not an executed FEA solver.
Original Lilerno illustration. Inputs are illustrative; this is not experimental evidence or a design rating.
| Series | Position along bar (m) | Displacement (mm) |
|---|---|---|
| Exact displacement | 0 | 0 |
| Exact displacement | 0.0125 | 0.0000625 |
| Exact displacement | 0.025 | 0.000125 |
| Exact displacement | 0.0375 | 0.0001875 |
| Exact displacement | 0.05 | 0.00025 |
| Exact displacement | 0.0625 | 0.0003125 |
| Exact displacement | 0.075 | 0.000375 |
| Exact displacement | 0.0875 | 0.0004375 |
| Exact displacement | 0.1 | 0.0005 |
| Exact displacement | 0.1125 | 0.0005625 |
| Exact displacement | 0.125 | 0.000625 |
| Exact displacement | 0.1375 | 0.0006875 |
| Exact displacement | 0.15 | 0.00075 |
| Exact displacement | 0.1625 | 0.0008125 |
| Exact displacement | 0.175 | 0.000875 |
| Exact displacement | 0.1875 | 0.0009375 |
| Exact displacement | 0.2 | 0.001 |
| Exact displacement | 0.2125 | 0.001063 |
| Exact displacement | 0.225 | 0.001125 |
| Exact displacement | 0.2375 | 0.001187 |
| Exact displacement | 0.25 | 0.00125 |
| Exact displacement | 0.2625 | 0.001313 |
| Exact displacement | 0.275 | 0.001375 |
| Exact displacement | 0.2875 | 0.001437 |
| Exact displacement | 0.3 | 0.0015 |
| Exact displacement | 0.3125 | 0.001563 |
| Exact displacement | 0.325 | 0.001625 |
| Exact displacement | 0.3375 | 0.001687 |
| Exact displacement | 0.35 | 0.00175 |
| Exact displacement | 0.3625 | 0.001813 |
| Exact displacement | 0.375 | 0.001875 |
| Exact displacement | 0.3875 | 0.001937 |
| Exact displacement | 0.4 | 0.002 |
| Exact displacement | 0.4125 | 0.002063 |
| Exact displacement | 0.425 | 0.002125 |
| Exact displacement | 0.4375 | 0.002188 |
| Exact displacement | 0.45 | 0.00225 |
| Exact displacement | 0.4625 | 0.002312 |
| Exact displacement | 0.475 | 0.002375 |
| Exact displacement | 0.4875 | 0.002437 |
| Exact displacement | 0.5 | 0.0025 |
| Exact displacement | 0.5125 | 0.002562 |
| Exact displacement | 0.525 | 0.002625 |
| Exact displacement | 0.5375 | 0.002687 |
| Exact displacement | 0.55 | 0.00275 |
| Exact displacement | 0.5625 | 0.002812 |
| Exact displacement | 0.575 | 0.002875 |
| Exact displacement | 0.5875 | 0.002938 |
| Exact displacement | 0.6 | 0.003 |
| Exact displacement | 0.6125 | 0.003063 |
| Exact displacement | 0.625 | 0.003125 |
| Exact displacement | 0.6375 | 0.003187 |
| Exact displacement | 0.65 | 0.00325 |
| Exact displacement | 0.6625 | 0.003312 |
| Exact displacement | 0.675 | 0.003375 |
| Exact displacement | 0.6875 | 0.003438 |
| Exact displacement | 0.7 | 0.0035 |
| Exact displacement | 0.7125 | 0.003563 |
| Exact displacement | 0.725 | 0.003625 |
| Exact displacement | 0.7375 | 0.003687 |
| Exact displacement | 0.75 | 0.00375 |
| Exact displacement | 0.7625 | 0.003812 |
| Exact displacement | 0.775 | 0.003875 |
| Exact displacement | 0.7875 | 0.003938 |
| Exact displacement | 0.8 | 0.004 |
| Exact displacement | 0.8125 | 0.004063 |
| Exact displacement | 0.825 | 0.004125 |
| Exact displacement | 0.8375 | 0.004188 |
| Exact displacement | 0.85 | 0.00425 |
| Exact displacement | 0.8625 | 0.004313 |
| Exact displacement | 0.875 | 0.004375 |
| Exact displacement | 0.8875 | 0.004437 |
| Exact displacement | 0.9 | 0.0045 |
| Exact displacement | 0.9125 | 0.004562 |
| Exact displacement | 0.925 | 0.004625 |
| Exact displacement | 0.9375 | 0.004687 |
| Exact displacement | 0.95 | 0.00475 |
| Exact displacement | 0.9625 | 0.004812 |
| Exact displacement | 0.975 | 0.004875 |
| Exact displacement | 0.9875 | 0.004938 |
| Exact displacement | 1 | 0.005 |
| Linear-element nodes | 0 | 0 |
| Linear-element nodes | 0.25 | 0.00125 |
| Linear-element nodes | 0.5 | 0.0025 |
| Linear-element nodes | 0.75 | 0.00375 |
| Linear-element nodes | 1 | 0.005 |
Save your place when you finish reading.
Original Lilerno example
An ideal linear elastic axial bar has F = 100 N, L = 1 m, A = 10⁻⁴ m² and E = 200 GPa. Predict elongation for a solver check.
Convert E to 200 × 10⁹ Pa.
Use δ = FL/(AE).
δ = 5 × 10⁻⁶ m = 0.005 mm.
Test the model
Open learning, traceable sources
Work in this order. These links open the publisher’s material; free access does not always permit republication.
Guido Dhondt and Klaus Wittig
Start with: Documentation and example problems
Start with a simple axial benchmark and compare displacement and reaction balance.
CFD Direct / OpenFOAM Foundation
Start with: Tutorials, meshes and boundary conditions
Read a small documented fluid case; compare a defined quantity under mesh refinement.
Recall, then record
Close the explanation and answer these in your own words. Return tomorrow, then again later in the week.
What is your validation evidence?
Which output is converging?
Could the peak be a singularity?
Write a simulation report template with model assumptions, boundary conditions, mesh study, reference solution and limitations. Do not launch heavy solvers merely to obtain a picture.
Self-reported tasks, not an assessment of mastery or university credit. Reading a page does not complete a chapter.
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Open learning, traceable sources
Original Lilerno lessons and diagrams, supported by these references. Free access does not always permit republication. Links open the publisher’s material.
Start with the tutorial and learn case structure, boundary conditions and mesh setup. A versioned guide, not a claim that v13 is the newest release.
Open-source solver; guide and software have separate notices. Linked only; verify the relevant documentation and code licence before redistribution.
Open source ↗Rights / publisher record ↗Existing structural solver, documentation and example problems. Compare a simple axial model with a hand calculation before attempting complex cases.
GPL-licensed software as stated by the project. Examples and linked documentation require their own notice checks. External tool; not installed or executed here.
Open source ↗Rights / publisher record ↗