Bending a circular five-layer plate by local load

The bending of an elastic circular five-layer plate under the action of a local transverse load distributed in a circle was studied. The plate, symmetrical in thickness, has three thin load-bearing layers (two external and one internal), the deformation of which obeys Kirchhoff’s hypotheses. In two relatively thick fillers, the normal remains straight and does not change its length, but rotates through some additional angle. The system of differential equations for the equilibrium of the plate was obtained by the Lagrange variational method. The analytical solution of the problem is written in Bessel functions in final form. Numerical results of the study of deflections and relative shifts are presented depending on the radius of the force circle, the thickness of the internal load-bearing layer, and the materials of the external load-bearing layers.