Maximum stress and deflection of a round diaphragm under pressure

dia        diameter of the diaphragm in µm
thc         thickness of the diaphragm in µm
pre        applied pressure in psi
ymod    Young's modulus of the material in GPa
pois       Poisson's ratio
sel         number denoting the selected result.
              Use 1 for maximum stress, 2 for maximum strain and 3 for center deflection


Diaphragms or membranes as it is sometimes called, form the basic structural element of MEMS pressure sensors. They are easy to fabricate, offer good dynamic response and can be used over a wide range of pressures.

This design interface can be used to determine the maximum stress and deflection of a round diaphragm.  In this analysis the outer perimeter of the diaphragm is held firmly and a uniform pressure is applied from top. The applied pressure will deflect the diaphragm till the elastic forces balance  the pressure. The maximum displacement is at the center of the diaphragm. At every point on the diaphragm, there is a radial as well as tangential stress. The maximum stress is the radial stress found at the outer perimeter of the diaphragm. The maximum strain is also the corresponding radial strain. The deflection and stress is slightly lower than that of a square membrane of equivalent size and thickness.

The plot shows the radial and tangential stress distribution over the surface of the diaphragm along a line passing through its center. It shows that the maximum stress is at the outer edge which is positive and tensile. This decreases and crosses over into a negative or compressive stress which reaches a maximum at the center of the diaphragm. This is for the top fiber of the diaphragm for top side pressure. Using the cross hair tool, the radial and tangential stress at any location along the diameter of the diaphragm can be estimated.

The 2D and 3D surface plots show the deflection of the membrane under pressure.


-The default material is Silicon with a Young's modulus of 180GPa and Poisson's ratio of 0.3.
-The diaphragm has round surface with uniform thickness.
-The diaphragm is assumed to be held rigidly at the outer perimeter. In reality it may be slightly flexible.
-The property of the material remain constant across the diaphragm.
-The diaphragm is not subjected to any pre-stress and the pressure is the only load acting on it.
-Bending effects are considered. Non-linear effects due to tension is ignored.
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