Module 15
Structural optimisation
Topology, layout, shape and size — and a measure that lets you compare layouts before a single member has been chosen.
What this module covers
- State an optimisation problem as objective, variables and constraints
- Distinguish topology, layout, shape, form-finding and size optimisation
- Compute a structural volume by Maxwell's load path and say what it omits
- Explain why the topology constant is invariant and what makes the comparison fair
- Iterate a size optimisation and explain the snowball
- Say why the lightest structure is rarely the one to build
Lessons
Objective, variables and constraints — and the four kinds of structural optimisation, which are not interchangeable.
Start lesson →Maxwell's load path: a structural volume computed from an analysis you have already run, and an invariant that makes the comparison fair.
Start lesson →Moving the nodes, choosing the members, and letting equilibrium choose the geometry.
Start lesson →
Module checkpoint
Check what you have taken in
3 questions
Question 1
Why can two bracing layouts have different structural volumes but the same topology constant?
Question 2
An X-braced bay and a single-diagonal bay both return a structural volume of 1 733 kN·m under the same load. If the X-bracing has two diagonals of equal length carrying equal force, what fraction of the single diagonal's force does each X diagonal carry?
Question 3
A size optimisation on an indeterminate truss changes the areas by 18 %, then 6 %, then 2 %, then 0.7 % on successive passes. By what factor is the change reducing each pass, approximately?