Computational Engineering / Parametric thinking

What a parameter is

Independent and dependent quantities, rules instead of coordinates, and why the choice of parameters is the design.

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Why this matters

A model built by typing coordinates answers one question: what does this structure do. A model built from rules answers a family of them.

That sounds like a change of technique. It is really a change of what you are designing. Once the model is parametric, the object you are designing is the rule set — and the rule set is where the engineering judgement now lives.

Independent and dependent inputs

An independent input is set by the user, such as span or roof pitch. A dependent quantity is calculated from the inputs and rules, such as a node coordinate or member length.

The inputs must respect their relationships. For a building with equal storey heights, overall height equals storey count times storey height. A model may set two of these and derive the third, or fix further values as constraints. It should reject inconsistent combinations and make clear which quantities are derived.

Rules and coordinates

A portal frame can be described by span, eaves height and roof pitch, with a rule placing the ridge at mid-span. The ridge height is the eaves height plus half the span times the tangent of the pitch. Changing an input then regenerates the coordinates using the same relationship.

Coordinate data records a particular geometry. The generating rules make the intended relationships explicit and allow controlled variations.

Choosing parameters

Five parameters with ten possible values each give 100,000 combinations. Estimate the cost of a complete sweep before choosing a search method. Module 16 covers search strategies.

Use sensitivity studies, as in Module 14, to identify which inputs affect the chosen outputs over the ranges of interest. Parameterise the quantities you need to investigate, state what is fixed, and retain uncertainty where it may affect the decision. A small set of inputs may dominate a particular response, but that should be demonstrated.

Keeping the model readable

Name and group the inputs. Record units, valid ranges, dependencies and the purpose of each rule. Another engineer should be able to trace how a changed input affects the geometry and analysis without relying on the author's memory.

Try it

Portal frame generator

Three independent parameters generate the whole frame. Everything else on the readout is computed.

Spanm

Eaves heightm

Roof pitch°

Set to zero for a flat roof and watch the ridge height collapse onto the eaves.

Span (set): 24.00 m
Eaves height (set): 7.00 m
Pitch (set): 6.0°
Rise (computed): 1.261 m
Ridge height (computed): 8.261 m
Rafter length (computed): 12.066 m
Frame member length: 38.13 m

What to notice

Three numbers are set and four are computed. The computed ones cannot be edited, because editing them would let you express a frame that does not exist.
Set the pitch to zero and the ridge collapses onto the eaves. The rule still holds; the geometry has simply become a flat portal.
The member length is not a design quantity. It is a comparison quantity, and its whole value is that it updates the instant a parameter moves.

What this shows: Rules generate coordinates; coordinates do not generate rules — and only two of a related triple may be set independently.

Check yourself

A parametric tower model exposes height, number of storeys and storey height as three independent sliders. What is wrong?

Worked example

Which of these is actually a parameter

Given

A parametric model of a warehouse is proposed with: span, bay spacing, eaves height, roof pitch, number of bays, portal frame or truss, and the steel grade

Find

Which are parameters, which are constants, and which is neither

Worked example

A parameter with no consequence

Given

A parametric tower model exposes twelve parameters
Varying one of them — the fillet radius on a connection plate — changes nothing in the analysis output

Find

What to do about it

Practice

A parametric model has 5 parameters, each taking 6 values. How many distinct designs does that define?

Check yourself

What distinguishes a parametric model from a model you can edit?

Check yourself

Why should a parametric model state what it has fixed?

Check yourself

A rule in a parametric model contains an error. How does that differ from the same error made by hand?

Summary

A parameter is an input others are derived from
Independent parameters are set; dependent ones are computed, and only one of a related triple may be derived
Rules generate coordinates; coordinates do not generate rules
Parameterise what you will vary or are uncertain about, and fix the rest explicitly
An unreadable parametric model has one user and a short life