Theory of plates

[gtsolid]

Hi,
i wish to calculate the maximum deflection of a squared plate supported in 4 points.
i'm able to find the pure bending of plates, but don't know very well how to consider the 4 points.

 

[Andries]

Where are the 4 points? Are they unequally spaced or at the corners? In the last case you could try Timoshenko and Woinowsky-Krieger: Theory of Plates and Shells. The book contains solutions for rectangular plates with the standard boundary conditions.

Andries

 

[gtsolid]

They are at the corners. I have that book, I think the correct section is 49. Rectangular Plates Having Four Edges Supported Elastically or Resting on Corner Points with All Edges Free.
My load is static, so i think i can delete terms with sinusoidal functions

 

[rb1957]

FEA ?

another day in paradise, or is paradise one day closer ?

 

[swimfar]

gtsolid,

Is the equation that you are looking at an infinite sum of terms? If so, those sine/cosine functions have nothing to do with dynamics. They are essential terms of the analytical solution.

 

[LiftDivergence]

gtsolid,

It appears you have already found the solution you are looking for. Timoshenko's book mentioned above, page 220 Table 48 has computed results for coefficients of a deflection equation for the center of the plate and a point half-way to the edge for the special case of a square plate under uniform pressure load and supported by elastic beams which all have the same flexural rigidity.

So, as long as your condition is approximated by this, you should be OK. As swimfar says, those trigonometric terms have nothing to do with dynamics. But Equation (a) on page 219 which I think you are looking at is the general case before he equates the edge moments to zero.

I think you can just use Table 48 to read off a value of alpha for whatever your gamma comes out to be. Then put that into the equation for w provided in the table.

Note this table is for nu = 0.25. However, he has some discussion in there that the deflection is not particularly sensitive to this.

Keep em' Flying
//Fight Corrosion!

 

[prex]

gtsolid, you could try this one: there are also other loading conditions and you can combine them. To use those sheets you will have to register and copy the sheets of interest into the private space, but it's free.

prex
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