Study On Bi-Material Superposed Cantilever Beam Subjected To Concentrated Force

Based on the basic equation of the plane elasticity problem, the analytical solution is presented for a bi-material superposed cantilever beam subjected to a concentrated force at the free end by using the stress function method. The solution of the stresses can be degenerated into the one of the single material cantilever beam subjected to a concentrated force at the free end, which can be found in the literatures. The study shows that the bending normal stresses in each layer of the bi-material superposed cantilever beam vary linearly along the height of the layer, the compressive stresses are zero, the shear stresses vary parabolically along the height of the layer. After deformation, the cross sections are not planes again, the shear force and bending moment in each layer of the beam are distributed based on stiffness ratio, and the external force acted at the free end of the upper layer must be not less than a certain value to maintain the contact between the upper layer and the lower one.In order to verify the correctness of the analytical solution obtained in this paper, different computing models of the superposed cantilever beam are calculated numerically by using the finite element software ANSYS10.0. The numerical results coincide with the analytic ones well, which verifies the correctness of the analytical solution. A further proof of the correctness of analytical solution is obtained by comparing others'experimental results with the analytic ones.