Abstract
The divergence part of the energy functional for an elastically isotropic plate is replaced by a boundary integral, thus showing that the energy functional of a simply-supported Kirchhoff plate under a surface load approaches that of a circular plate with clamped boundary conditions. This conclusion does not depend on series solutions, singularity analysis, or elaborate, three-dimensional functional analysis.
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Simmonds, J.G. A Simple Energetic Explanation of the Polygon-Circle Paradox for Classical (Kirchhoff) Plate Theory. J Elast 99, 113–116 (2010). https://doi.org/10.1007/s10659-010-9240-2
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DOI: https://doi.org/10.1007/s10659-010-9240-2