Based on Fourier series, we adapt an approach discussed in a recent work
on the Laplace operator to classical results obtained in the literature,
describing the singularities of solutions to a fourth-order elliptic
problem on a polygonal domain of the plane that may appear near a
concave corner. We demonstrate how the Fourier series method provides
explicit decomposition and precise description of the coefficients of
singularities of the solution. As a main result, explicit and sharp
estimates with respect to the opening angle parameter can be obtained
via this method. We recall that such estimates can be useful for the
asymptotic analysis of solutions near corners where the opening angle
generates a jump in singularity in Sobolev's exponent.