ANALYTIC SOLUTIONS TO THE BENDING PROBLEM OF RECTANGULAR THIN PLATES SIMPLY SUPPORTED ON FOUR SIDES ON A WINKLER FOUNDATION WITH HORIZONTAL FRICTION

Assuming that the horizontal friction between the plate and the foundation is proportional to the horizontal displacement difference between them, the differential equations for a rectangular plate resting on an elastic foundation with horizontal friction were established according to the force equilibrium and the constitutive relationship, and the analytical solution in series form was obtained for the four-side simply-supported plate. The effects of the horizontal friction on the deflection and bending moment of plates were analyzed by taking the concentrated load and the square uniform load acting at the center of the plate as examples. The results indicate that the horizontal friction between the plate and the foundation has a reduction effect on the deflection and bending moment of the rectangular plate. When the horizontal friction parameter is greater than 0.01, the influence of the horizontal friction on the deflection and bending moment may exceed 2% and should be considered. The size of the plate and the size of the load affect the reduction effect of the horizontal friction, which should be considered carefully according to the actual working conditions. When a square uniform load is applied at the center of a square plate with a relative length of 5, the horizontal friction can cause the maximum deflection of the plate (i.e., the deflection at the center of the load) to decrease by about 60 %, and the maximum section bending moment (i.e.,the bending moment at the center of the load) to decrease by about 70 %.