Nonlinear analysis of circular plates on elastic foundation 2

[mr7755]

Hello Dear sir/madam
Does any body know about the topic written above?
Any reference or any published document?
(Nonlinear analysis of thin circular plates on an elastic foundation under symmetric mechanical loading)

 

[connect2]

What do you mean by 'Mechanical Load'? I have to say you've got it all there, non-linear plate analysis, and elastic (one assumes Linear) foundation, glad you have the word 'Symmetric'in there?

 

[Denial]

It would also help to know what sort of non-linearity you are dealing with: material? geometric? foundation?

 

[mr7755]

Thanks connect2 and denial
From nonlinearity I mean " geometric nonlinearity"
From elastic foundation I mean " Linear elastic foundation"
and from 5mechanical load I mean " Symmetric outer pressure loading, P = P(r)"
regards

 

[Denial]

I am unaware of any texts on non-linear analysis of circular plates on an elastic foundation under the action of radially symmetric loading.

If you are prepared to ignore non-linear behaviour, see "Theory of Plates and Shells" by Timoshenko & Woinowsky-Krieger, where there is an entire chapter devoted to plates on elastic foundations. Most of the chapter assumes that the foundation behaves in a "Winkler" manner, ie that the foundation has no elastic continuity. (Such a foundation is sometimes referred to as a "liquid" foundation.) The first case the chapter investigates is your case of radial symmetry in both the structure and the loading. Even with the Winkler assumption, the mathematics gets pretty heavy pretty quickly.

If you must have your non-linear behaviour, then Roark's "Formulas for Stress and Strain" gives the barest of outlines on an iterative method. This allows you to take an analysis method that initially ignores the effects of the elastic foundation (still a Winkler foundation) and gradually extend the result to incorporate more and more of the foundation reaction. It should be equally applicable to non-linear behaviour in the plate.

Please post the details if you find a better reference somewhere.

HTH

 

[connect2]

good. thought 'mechanical load' might mean dynamic. Yes exactly Denial the consideration is non-linear plate behaviour and linear-elastic soil interaction.
This is a topic well outside a chat group but to head in the right direction one must be able to predict the soil-structure interaction and specifically the deformation in the soil, it self a crap shot, i mean really trying to get a Modulus of Sub-Grade reaction Ks out of a Geotech is tough enough ... Winkler springs and linear elastic soil behavoir is way out there when trying to model 'Real World' behaviour, but useful..
Try these;
1)Beams on Elastic Foundations, V.Z. Vlasov, N.N. Leont'ev
2)Formulae, Charts and Tables in the Area of Soil Mechanics and Foundation Engineering stresses in Soils, A. Teferra, E.Schultze.
3)Tabulated Values for Determing the Complete Pattern of Stresses, Strains and Deflections Beneath a Uniform Circular Load on a Homogeneneous Half Space, R.G. Ahlvin and H.H. Ulery
4)Stresses and Displacements in a Cross-Anisotropic Soil, L. Barden.

Suppose once you know the behaviour of the subsoil you'll be able to predict the behaviour of the plate, mean after all if it was on founded on bedrock we wouldn't be having this discussion ... but yes the stiffness of the plate and its boundry counditions will influence the displacement and stress distribution in the sub-soil and on we go ....
homogeneous elastic half-space would be nice, it certainly has a ring to it.

What are you actually designing?

 

[mr7755]

Thanks Denial and Connect2
I found a great reference:
"Nonlinear Analysis of Plates" by Chia
Regards