Origami / geometry that carries a load Independent research · Mechanical benchmark 01
Archived benchmark 01 · folds held fixed. Open the flexible-fold experiment →
A crease changes the answer.
A sheet sags. Fold it, and it becomes a bridge.
What did the fold actually change?
No extra material. No thicker sheet. The fold moves material away from the middle of the cross-section, where it can do more to resist bending.
This experiment starts with a precise question: does adding more creases help? Compare three arrangements of the same sheet. Change the angle, apply a load, and follow the geometry into the calculation.
O–01 / The folded bridge
Same sheet. Different depth.
Ideal elastic sheet · E = 2 GPa
Small-deflection screen: checking…
Live calculation using a locked cross-section and linear beam bending. The supports permit end rotation. The central load is distributed across the section by an ideal rigid spreader. Fold angle changes the reference geometry; loading does not open the creases. Displacement magnification is displayed explicitly.
01 / The surprise
More creases.
Less height.
Fold the same strip into a single ridge, then into a fine accordion. At the same panel angle, both cover the same width. But the accordion’s shorter panels cannot rise as high.
For this family, the part of bending stiffness created by the fold falls with the square of the panel count. Doubling the number of panels quarters that contribution. The sheet’s thickness still contributes a small baseline.
That is the lesson to carry forward: counting folds throws away the relationship that matters here. Their depth relative to the bending axis is what enters the calculation.
Where the material goes
Teal: sheet centerline. Dotted: neutral axis, where longitudinal bending strain is zero. End views use one common scale.
02 / Compare without changing the rules
The same test, four answers.
This comparison updates with your angle and load. All cases have the same material, thickness, developed sheet width, 360 mm span and total force. The three folded cases also have the same projected width. The flat sheet occupies more width.
| Arrangement | Fold height | Width | Stiffness / flat | Center displacement |
|---|
A little depth goes a long way.
Each curve starts at the same flat sheet. The vertical scale is logarithmic: each step means ten times the stiffness.
— 2 panels— 4 panels— 8 panels
03 / The calculation beneath the picture
Geometry enters through I.
The second moment of area, I, measures how far the material sits from the neutral axis. Material farther away contributes more because that distance is squared. Multiplying by the elastic modulus, E, gives the beam’s bending stiffness.
Here the sheet becomes n equal longitudinal panels. Each panel tilts by angle α from horizontal. The model integrates the rotated rectangular panels about their shared horizontal neutral axis.
h = (B / n) sin α
I = (Bt / 12) [(B / n)² sin²α + t² cos²α]
δ = PL³ / (48EI)
B: developed width · t: thickness · h: centerline fold height · L: span · P: central force · δ: center displacement. Dimensions are in mm; forces in N; E in N/mm².
David Roylance / MIT · Beam Displacements ↗What is actually tested?
- The flat limit recovers the ordinary rectangular sheet.
- Developed width and material volume stay constant during folding.
- Independent numerical area integration checks the section formula.
- A beam stiffness-matrix calculation checks the displacement at three mesh resolutions.
- Zero load, support conditions, symmetry and load scaling are checked separately.
Read the downloadable validation record below.
Open the checks and 183 angle cases →04 / From a stiff shape to a useful object
Can it keep its shape?
That is the next experiment. The calculation above holds the cross-section fixed. A real folded sheet may flatten at a crease, twist, buckle locally or tear before this bending model predicts trouble.
I want to measure which fold relationships preserve the available load paths—and which unlock a motion that makes the structure give way. This classical benchmark gives that investigation a reference it has to reproduce before adding more mechanics.
The boundary of this result
The reference material is homogeneous, isotropic and linear elastic. Its 2 GPa modulus is a declared input, not a measurement of a particular paper. Self-weight, crease compliance, joint overlap, plasticity, contact and local buckling are omitted.
A displacement above L/50 is flagged as outside a conservative small-deflection screen. Passing that screen does not establish stability or load capacity. The animation is a sequence of static solutions, not a dynamic impact simulation.
This first benchmark establishes the classical reference calculation for the broader origami investigation.
05 / Take the calculation apart
Every curve has a source.
Independent computational exploration · 26 October 2026 · Benchmark 01