Hallo,
i would like to know how do i calculate the deflection of non uniform Circular Plate. I have solved the same problem for beam with non uni form cross section. However in case of circular i guess there should be a clear way of doing it analytically.
Hi,
It depends how you mean by non uniform term if you mean step step cross section (piece wise) we have exact solution but if you mean linear or nonlinear cross section profile, I think there is no exact method however you can use Ritz or GDQ method to find solution.
Hallo,
@Ilkhani: thank you for replying, i am sure that one can solve it through the von Karmen theory but i have diffeculty in managing the simposons integration with respect to Theta. the goal was to an clear approach of solving it. Thanks in Advance.
Hallo,
@Bhrami, this is idealization of the real case. exact solution can actually be obtained for all but i am not so clever in multivariable function integration). Thanks in Advance
Hi Tamer Qaimari,
if you are going to analyze the deflection and stress resultants, the plate is relatively thin and you are not interested in stress concentrations (singularities) in corners, so you may apply the Kirchhoff plate theory or Mindlin/Reissner type theories. For axi-symmetrical case (plate and loads) you have to solve 4th-order ODE for Kirchhoff plate and 6th-order ODE for Mindlin plate. I attached some pages from our book Ebene Flächentragwerke, Springer, 1998, where the general solution for Kirchoff plate is presented. Consider two plate rigs- the outer and the inner, and apply boundary and transfer conditions to find 8 constants. I think it would take some time, but you can derive a closed-form solution. Take a symbolic processor, like Mathcad, to accelerate computations. A similar example is given in pp. 237-239. Please consult the books of Szilard, may be you find a problem similar to your solved there.
Hallo Prof. Naumenko,
Thank you very much. I will take a closer look into the Attached file. I am using scilab for the moment, i hope solving it this weekend. I will do inform you if i find a solution. Have a nice weekend. Tamer
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