FROM A BUCKLED STRIP TO A FOLDED TUBE
Geometric elasticity: how thin things bend, buckle and snap
A thin sheet can bend for almost nothing, but stretching it costs far more. That one fact explains why a clamped strip buckles into an arch, why the arch jumps when pushed, why a growing disc curls into a dome and why a folded paper tube can click into a second shape and stay there. Each chapter derives one of these and checks it in a Lab.
A strip between two clamps · Chapters 1–4
Bend, buckle, snap
Find out why thin things bend instead of stretching, buckle a clamped strip into an arch, push the arch until it jumps, then work out how fast the jump grows and how the strip rings afterwards.
Start with a thin strip →Shape from geometry · Chapters 5–8
Growing discs and folded tubes
Give a disc lengths that no flat sheet can hold and find the thickness where it gives up and curves, fold a Kresling tube that clicks into a second shape, then read the snapping-beam paper figure by figure.
Start with a growing disc →Eight chapters, with examples and experiments
01 L1
Why a thin sheet bends instead of stretching
Why does a sheet of paper bend at a touch but hardly stretch at all?
Read and try →02 L2
A clamped strip buckles into an arch at the Euler load
How far must the ends of a clamped strip be pushed together before it buckles, and how high does the arch then rise?
Read and try →03 L2
Pushing an arch until it snaps
When a blade pushes a buckled strip slowly down, where does the strip jump, and why there?
Read and try →04 L3
How fast a snap happens
Once the blade lets go, how long does the strip take to snap, and what sets that time?
Read and try →05 L2
Growth that no flat sheet can hold
What does it mean for growth to give a sheet a curved geometry, and why can no flat sheet have it?
Read and try →06 L3
The thickness where a disc buckles
A disc is asked for a curved geometry. Below what thickness does it leave the plane, and how does its energy split once it has?
Read and try →07 L3
Kresling folds and their stress-free shapes
Why does a twisted origami tube stay folded with nothing latching it, and which designs spring back instead?
Read and try →08 L4
Reading the snapping-beams paper
What does each figure of Pandey et al. (2014) show, how was it obtained, and which of its numbers can a reader check?
Read and try →