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I would like to calculate the displacement function of a circular plane with a circular hole in the center, along which it is interlocked.

I thought about solving with the following code:

domain = ImplicitRegion[x^2 + y^2 <= 4^2 && x^2 + y^2 >= 2^2, {x, y}];
pde = D[w[x, y], {x, 4}] + 2 D[w[x, y], {x, 2}, {y, 2}] + D[w[x, y], {y, 4}] == 1;
bcs1 = DirichletCondition[w[x, y] == 0, x^2 + y^2 == 2^2];
bcs2 = DirichletCondition[D[w[x, y], {x, 2}] == 0, x^2 + y^2 == 2^2];
bcs3 = DirichletCondition[D[w[x, y], {y, 2}] == 0, x^2 + y^2 == 2^2];
NDSolveValue[{pde, bcs1, bcs2, bcs3}, w[x, y], {x, y} \[Element] domain]

but unfortunately I get the following error:

NDSolveValue::femcmsd: The spatial derivative order of the PDE may not exceed two.

Can you correct me, please? Thank you!

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    $\begingroup$ I'm voting to close this question as off-topic because the OP is asking for functionality that Mathematica does not currently support. $\endgroup$ – m_goldberg Dec 3 '17 at 1:36
  • $\begingroup$ Sometimes I want to delete some topics because I realize I'm wrong with the approach. Sorry. $\endgroup$ – TeM Dec 3 '17 at 12:23
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It's partially explained in the similar question. Since you use regions, Mathematica has to go for FEM solver. Unfortunately, its FEM solver doesn't support derivatives greater than 2 (that's what the error message is about).

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