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Computational Engineering / 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 you will understand

  • 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

  1. Posing the problem

    Objective, variables and constraints — and the four kinds of structural optimisation, which are not interchangeable.

  2. Comparing layouts before sizing

    Maxwell's load path: a structural volume computed from an analysis you have already run, and an invariant that makes the comparison fair.

  3. Shape, size and form

    Moving the nodes, choosing the members, and letting equilibrium choose the geometry.

Module summary
  • Objective, variables, constraints — write all three or you have not posed a problem
  • Topology decides what connects to what; shape moves the nodes; size chooses the members
  • Structural volume is Σ|F|·L and it needs no section sizes
  • For fixed loads and supports the tension minus compression load path is invariant
  • Sizing changes the forces, so one pass is never the answer in an indeterminate structure
  • A fully-stressed design is exactly critical everywhere, which is not the same as robust
  • Repetition, connections and buildability are outside every measure in this module
Teaching basis and review status

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 notes

Check your understanding

Check yourself

Why can two bracing layouts have different structural volumes but the same topology constant?

Practice

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?

Practice

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?