When a UDL is acting on the ends of circular plate as shown in attached drawing, how to calculate the deflection at end of the plate when it is fixed at center.
hi
your problem can be easily solve by FEM software (e.g. ABAqus).
if you need further help, please let me know
As Raafat says, the fastest way is to use a FEM tool. There are a lot that are freely available.
Franco
Luckily, the problem is axisymmetric. Its analytical solution based on the classical plate theory can easily be found in the literature. See, for example, formulas given in "Plates and Shells" by Timoshenko or "Roark's Formulas for Stress and Strain" by Young and Budynas.
A more accurate analysis can be performed using the finite element codes taking into account transverse shear strains and contact interaction between the structural members.
You can assume it as a cantilever beam with varying cross section from center to edge of the plate. Later you can also do a FEA to validate the results.
@Vinit, IMHO taking it as a cantilever beam with varying cross section is not a good assumption. By doing that you will ignore the circumferential stresses. We must use plate theory including membrane stresses.
You can use a FE program to model the plate using shell element. Unfortunately, there will be differences in bending stiffness of various shell element types used. The standard 4-node DKQ element used by most programs will give more than 10 pct difference to analytical solution. The best shell element for bending is Quad4 Hybrid stress or ANDES shell element. If available you can use higher order element such as QPB8 or QPB9.
As i see in drawing,it is not a plane stress problem.
U must be use 3d elasticity formulation to solve that.
This like a bushing in cylnder or pump rod.
The problem is a plate bending problem, if the center shaft is not modeled together but defined as circumferential support of the circular plate. If the center shaft is also modeled, then we must use solid modeling using brick or tetrahedron elemen.
If thickness/radius ratio of the plate is less than 0.1 then it can be considered as plane stress. In that case shell elements can be used and also analytical formulation (as given in my first comment) can also be used provided the deformations/displacements remain small and elastic.
If the thickness/radius ratio is greater than 0.1 then the through thickness stress and transverse shear cannot be neglected and it is better to use 3D elements.
As mentioned by Stanislav, since the problem is axissymetric, the best way is to use an axissymetyric FEA model. However, with axisymmetry we may miss some results for e.g. if wrinkles appear in reality we may not see those in the simulation results.
In case the shaft is modeled (though i dont think it is necessary) then one must use 3D elements for the shaft.
the flange which I have shown in the fig has undergone plastic deformation which was mounted on shaft and the deflection which is measured is 7 mm.
I want analytical method for solving the above problem. as i have to include both in my report.
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