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Flat-Plate Deflection

A pressure-loaded plate is governed by its flexural rigidity D = Et³/(12(1−ν²)). Deflection goes as the fourth power of radius and the inverse cube of thickness — thickness is by far the strongest lever.

Pressure q (MPa)

Plate radius a (mm)

Thickness t (mm)

Modulus E (MPa)

Poisson's ν

Edge condition

Max deflection

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Max stress

—

Flexural rigidity

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Small-deflection (linear) theory — valid while deflection is under about half the thickness. Beyond that membrane stiffening makes the plate stiffer than this predicts.

A helper, not a substitute for engineering judgment. Verify against the governing standard.