Three-point bending of a short beam with symmetrically varying mechanical properties

The subject of the paper is a short beam with symmetrically varying mechanical properties. The values of elastic modules vary in the depth direction of the beam. The nonlinear shear deformation theory is assumed i.e. the hypothesis for plane cross section. Based on the principle of stationarity of total potential energy three differential equations of equilibrium are obtained. The system of equations is solved for three-point bending of the beam with the use the trigonometric series. The shear stresses distribution in the cross section of the beam and the deflections are determined. Moreover, numerical - FEM model of the beam is developed and the shear stresses distribution and the deflections of the beam are calculated. The results of these two methods are compared.