RCTDIA,len,wid,thc,pre,pois,ymod,sel
Maximum stress and deflection of a rectangular diaphragm under pressure

len         length or longer edge of the diaphragm in m
wid        width or shorter edge of the diaphragm in m
thc         thickness of the diaphragm in m
pre        applied pressure in psi
pois       Poisson's ratio
ymod    Young's modulus of the material in GPa
sel         number denoting the selected result.
              Use 1 for maximum stress, 2 for maximum strain and 3 for center deflection

Notes

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 rectangular diaphragm.  In this analysis the outer edges of the diaphragm are 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. The maximum stress happens at the middle near the edge of the diaphragm. If we consider a point there, it will have a stress directed towards the center (0,0) of the diaphragm, which we will refer to as radial stress. There is also a stress perpendicular to it which is the tangential stress. The radial stress is higher than the tangential stress at that point. The maximum stress given is the radial stress and the maximum strain is the corresponding strain at that point.

The plot shows the radial and tangential stress distribution over the surface of the diaphragm along a line passing through its center and the middle of the longer side of the diaphragm. This line is parallel to the width of the diaphragm. 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.

Assumptions

-The default material is Silicon with a Young's modulus of 180GPa and Poisson's ratio of 0.3.
-The diaphragm has rectangular surface with uniform thickness.
-The diaphragm is assumed to be held rigidly at the outer edges. 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.
-The location of the maximum stress may vary slightly based on the boundary condition.
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Mechanics > Structures > Diaphragms > Rectangular Diaphragm


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