We proposed a new theory of bending of axisymmetrically loaded plates in the form of thick rings or disks for the case where their deflections are not large and the stressed state is not described by the Kirchhoff–Love or Timoshenko hypotheses. For bending of this kind, we use two harmonic functions that describe the axisymmetric stressed state. After integration over the thickness of the plate, the momentsand transverse forces are expressed via two functions. The relationships of the theory of elasticity are exactly satisfied and a closed system of equations for the introduced functions is constructed without using any hypotheses about the geometric nature of deformation of the plate. A method for the solution of these equations is developed. We also present the solution of various problems of bending of the plates with holes.
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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 55, No. 4, pp. 22–26, July–August, 2019.
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Revenko, V.P. Bending of Axisymmetrically Loaded Thick Plates. Mater Sci 55, 477–483 (2020). https://doi.org/10.1007/s11003-020-00328-x
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DOI: https://doi.org/10.1007/s11003-020-00328-x