Analytical And Numerical Research On Superposed Cantilever Beam Under Uniform And Linear Loads

Based on the basic equation of plane elasticity, this paper provides both analytical andnumerical researches for two-layered superposed cantilever beams under uniform or linearload on the upper surface by using the Airy stress function method. The study shows asfollows.The elasticity solutions are deduced for the stresses and displacements of two-layeredhomogeneous superposed cantilever beam when subjected to uniform or linear loads on theupper surface. For the beam subjected to uniform load, two kinds of the simplified methodsof free end are introduced and discussed. Moreover, the influence of friction on the contactbetween the two layers has also been included in the discussion. The research shows thatthe second kind of the simplified method is better, and the stress within the beam could bereduced by friction. However, such effect is so limited that it can be ignored and treated assmooth.The elasticity solutions are also deduced for the stresses and displacements oftwo-layered FGM superposed cantilever beam under uniform or linear loads on the uppersurface. A function of the location of neutral surface is introduced. The study shows that thelocation of the neutral surface would shift to the side with larger Young’s Modulus.In order to verify the correctness of the analytical solution in this paper, numerical studywas introduced to calculate different computing models of superposed cantilever beam byusing finite element software ANSYS12.1. The results are in accordance with the analyticalones, which verifies the analytical solution.