A Simple Energetic Explanation of the Polygon-Circle Paradox for Classical (Kirchhoff) Plate Theory |
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| Authors: | J G Simmonds |
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| Institution: | 1. Department of Civil and Environmental Engineering, University of Virginia, P.O. 400742, Charlottesville, VA, 22904-4742, USA
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| 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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