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!