Computational Engineering / From physical structure to analytical model
Choosing the level
Matching the question to the cheapest model that can answer it — and pricing the alternatives first.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Checks needed for project use
- A computational engineering reviewer must check algorithms, convergence claims, statistical assumptions and numerical examples beyond the cases explicitly recorded.
- A computational structural specialist should validate abstraction explorer equations, section assumptions and local-model limits before design use.
- Exact shell-node counts and runtime estimates require the actual mesh/solver; the course numbers remain illustrative.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
Choose a model whose formulation represents the behaviour needed for the question. Additional detail may help resolve local effects, but also increases the work needed to build and check the model. Compare suitable alternatives before committing to a level of detail.
By the end of this lesson you should be able to
- Match a question to the cheapest level that answers it
- Recognise that a model outside its range still returns a number
- Estimate model size at each level before committing
- Explain why a solid model is not an assumption-free model
Match the formulation to the question
Hand calculations may estimate member forces, deflection, buckling and natural frequency where a suitable idealisation exists. Line models can represent global frame behaviour, while shell and solid models can resolve additional local effects. The choice depends on geometry, loading and the response needed; no fixed table can assign every connection or ground-pressure problem to one element family.
A beam model may recover nominal bending and axial stresses, but those do not resolve a cope, notch or connection stress concentration. Use a local model or an applicable local design method when that is the question.
Estimate model size
For the illustrative six-storey, 4 × 3 bay building, the frame counts are 35 nodes for one 2D frame and 140 for the 3D frame. With three and six freedoms per node respectively, these give 105 and 840 unconstrained freedoms.
The exercise uses floor area divided by mesh spacing squared as an approximate shell count. At 0.5 m spacing it estimates 18,572 total nodes and 111,432 freedoms, about 133 times the frame count. This area-based estimate approximates cells or interior nodes; an exact node count must include boundaries, shared nodes and the mesh topology.
Solution cost depends on matrix sparsity, ordering, constraints, solver and hardware as well as freedom count. Use these estimates to plan the work, not to predict an exact runtime multiplier.
Remaining assumptions
A solid model still needs a constitutive law, boundary conditions, load application and adequate discretisation. More geometric detail does not validate those choices.
Before analysis, state which comparisons or observations would show that the chosen idealisation is inadequate. Those checks help decide whether to refine the model, change its formulation or investigate a local region separately.
Try it
Element and level selector
Choose a question. See which levels answer it honestly, what each discards, and what each would cost to build.
The question the model must answer
Cheapest level that answers this honestly: Hand calculation
| Level | Answers it? | Freedoms |
|---|---|---|
| Hand calculation | yes | 0 |
| Two-dimensional line model | yes | 105 |
| Three-dimensional line model | yes | 840 |
| Shell model | no — it would still return a number | 111,432 |
| Solid model | no — it would still return a number | 110,592 |
What hand calculation discards, permanently
- Continuity
- Load sharing
- Everything three-dimensional
How the freedom counts are arrived at
- No model. One span, one formula.
- One frame taken out of the building: 5 columns × 7 levels, three freedoms each.
- Every column line at every level: 5 × 4 × 7 nodes, six freedoms each.
- The frame plus a 0.5 m mesh over 6 floors of 768 m²: 3072 nodes per floor.
- The same mesh carried through 0.25 m of thickness in 2 layers, floors only.
What this shows: A model outside its range returns a number rather than a refusal — so the check has to happen before the question is asked.
Practice
A 3D frame model of the building above has 840 degrees of freedom and the shelled model has 111 432. By what factor does the model grow?
Practice
The shell mesh above is 0.5 m. If it is halved to 0.25 m, by what factor does the number of shell nodes increase?
Summary
- Most structural questions are answered several rungs below where people reach
- A model outside its range returns a number, not a refusal
- A shelled model of this building is 133 times the size of the frame model
- Mesh nodes go as the inverse square of the size in 2D, the inverse cube in 3D
- A solid model moved the assumptions; it did not remove them
- If no result would change your mind, a cheaper model would do as well