# Flat Plate Deflection & stress - HDPE

Hi,

I'm trying to carryout some analysis of flat plates subjected to hydrostatic water pressures however the plate material is HDPE.

The problem I'm having is that all the formulae on the web and in Roark's 7th Edition are typical of steel with a Poisson's ratio of 0.3. I can't therefore find how to change the formulae or constants to account for the larger Poission's ratio that would be expected with HDPE (0.38-0.4).

To keep things simple I'm just considering a rectangular plate with fixed edges and a uniform UDL over the whole area as opposed to a triangulated load.

Can anybody offer advice on how best to deal with the stress and deflection of an HDPE plate?

This is a good question. I know the errors in these formulas are no more than 3% for Poisson's ratio (PR) of 0.26 to 0.34 (REF: Machinery Handbook).

For the deflection, you can just use the same formula and the modulus of elasticity of HDPE.

For the stress, one possible method is as follows. From, the definition of PR, your HDPE will have a decease in diamater ("neck down") compared to PR=3 by the ratio: 0.4 / 0.3. So the area will decrease by the ratio: (0.4 / 0.3)^2 = 1.78.

Thus, for initial estimating, I would multiply the stresses you calculate by a factor of 1.78. Be sure to use a valid value of yield stress. And I would recommend limiting your loads to less than 40% yield stress.

EDIT:

I have a feeling my 1.78 factor on calculated stresses is too high (but will provide conservative results).

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Thank you, this will be a good starting point.