Reduction of a Three-Dimensional Problem of the Theory of Bending of Thick Plates to the Solution of Two Two-Dimensional Problems

Abstract

We propose a new theory of bending of thick plates in the case where its stressed state is not described by the Kirchhoff–Love or Timoshenko hypotheses. It is assumed that the three-dimensional stress-strain state of the plate can be split into symmetric bending and symmetric compression. To describe symmetric bending, we use three harmonic functions. Integrating over the thickness of the plate, we express the bending and torsional moments and shear forces via two two-dimensional functions. The relations of the three-dimensional theory of elasticity are satisfied and a closed system of sixth-order partial differential equations for the introduced functions is constructed without using any hypotheses about the geometric character of deformation of the plate. The analytic and numerical methods for their solution are proposed.