Point load on a rectangular plate on spring (Roark-like formulation)

[bdbd]

Hi, as written on the title, I am looking for a Roark-like case explained in a simple way: "Point load on a rectangular plate on spring." So, the bending and shear calculation for the plate sitting on a soil represented by linear uniform springs.

 

[centondollar]

The easiest way to solve this problem is by applying FEM software. Another option would be to use Rayleigh-Ritz method for the Kirchoff plate problem with a suitable trial function for the deflection, but finding the function might be difficult.

PS. A slab resting on uniform linear springs is not an accurate model (nor necessarily a conservative model, even if you low-ball the spring stiffness) of foundation-soil interaction, which I assume you're attempting with this model. You would need to increase the spring stiffness close to the slab edges for the solution to approximately replicate a theory of elasticity solution. I suggest you read this:

https://www.structuremag.org/?p=7840.

 

[bdbd]

The easiest way is not the way I am looking, I am looking for the function as you said in the second option. I'll have a look.
And without even knowing what I am doing, this out-of-shelf comment is just very interesting. I know how the springs work. Thanks for your concern.

 

[centondollar]

Here is an article highlighting the Fourier series coefficient for a point load (and other loads) on rectangular Kirchoff plate using uniform Winkler springs as support. The deflection fields are also solved for some cases, including the point load case. Found by googling "ritz point load winkler plate".

https://www.researchgate.net/public...angular_Kirchhoff_Plate_on_Winkler_Foundation