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I have a cantilever that is a plate (not a beam) with dimensions 2mm wide x 4mm long x 0.3mm thick. It is fixed only at one side, with the other 3 sides free. I want to be able to find the intrinsic stress on it after it is fabricated.

To complicate matters, I also want to put biological cells (which can be assumed as a thin film) on the cantilever plate and calculate the stress that the cells exert on it based on the measured deflection. Further, these cells also beat and exert a force on the cantilever.

Is it possible to be able to:

(1) Find the intrinsic stress based on measured deflection

(2) Find the stress caused by cells (as a thin film) based on measured deflection

(3) Find the force caused by beating cells (as a thin film) based on measured deflection

all for a 'plate cantilever'?

I've tried to study Timoshenko's book and look for similar equations in Rourke's book, but could not find one similar in this case. I know this sounds like 3 complicated cases, but would really appreciate some help if anyone has insight.

Thanks!

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# Plate cantilever stress and force theory

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