Give a block of material a place to stand and a load to carry, and ask it what shape it wants to be. It will not answer with a truss you recognise. It will hollow itself out, split into branches, open holes you never specified — and the arrangement it arrives at is stiffer than anything you would have drawn. What it is choosing is not a shape. It is a topology.
Stretch a square into a circle, a blob, a country. Bend it, taper it, wring it out. Some things survive every one of those deformations: how many separate pieces there are, and how many holes each piece has. Everything else — length, angle, area, curvature — is negotiable.
Those stubborn quantities are the topology of the shape. You cannot change them by pushing. You change them only by cutting or gluing. A coffee cup and a doughnut are the same object to a topologist, and a structural engineer should care, because a hole is not a detail you add at the end. It is a decision about how force is allowed to travel.
Draw. Erase. Watch the numbers refuse to move until you actually break something.
Here is a solid slab of material, clamped at the left, with a load you can move. Nothing is optimised; every element is fully present.
The colouring is strain energy — how hard each patch of material is actually working. Almost all of it is idle. The force carves a narrow corridor from where it lands to where it is resisted, and the rest of the slab is along for the ride: heavy, expensive, and structurally asleep.
Move the load and the corridor moves with it. Then switch to Load paths and watch the force actually travel: amber streams are compression — material pushing the load back toward the wall — and slate streams are tension, material gripping so the slab isn’t torn open. Every structure ever built is these two rivers negotiating a route.
Hang a second weight and watch the rivers merge. The path was never a property of the material — it is a property of the boundary conditions.
So take the idle material away. Solve, find the laziest elements, remove them, solve again. Repeat. This is the oldest idea in structural optimisation, and it is brutally simple.
Watch what happens to the count of holes. It starts at zero — a solid slab is topologically a disc. Then the slab tears open, and tears again, and the number climbs. Nothing instructed it to make holes. The holes are what's left when you subtract the parts that weren't carrying anything.
The structure did not get a shape. It got a topology, and the shape came with it.
Deleting elements is greedy: once a piece is gone it can never come back, and one bad early call scars the result. The modern method lets every element be partly there — a density between nothing and solid — and then makes being half-present expensive, so the field is squeezed toward a clean yes or no.
Give it less material and it does not merely shrink the same structure. It redesigns it: members merge, holes open, the whole layout reorganises. Slide the budget and watch the topology change, discretely, at thresholds — the same way a bridge type changes when the span gets long enough.
This is SIMP, and it is what every generative-design tool is running underneath.
Pin the supports where you want them, put the load where you need it, say how much material you are willing to pay for, and let it find the structure. Nothing about the answer is chosen by you — not the number of members, not the branching, not a single hole.
Try the bridge at a generous budget and then starve it. Watch the deck thin, the arch emerge, the spandrel open up. You are not adjusting a shape. You are changing which topologies are affordable.