Stress Analysis Of Bi-Material Superposed Beams

The superposed beams consist of two or more than two kinds of materials. The superiority of different materials can be exerted in strength, stiffness and corrosion resistance. Because of the features of flexible design and construction simple, the application in practical engineering is more and more widely.In this dissertation, based on the basic equations of plane elasticity, by using the stress function method, two kinds of equivalent boundary conditions are put forward for the simply supported end of bi-layer superposed simply supported beams, and the corresponding analytical solutions of the superposed simply supported beams with bi-layer isotropic materials and bi-layer orthotropic materials are obtained. Two kinds of equivalent boundary conditions have effect on the bending normal stress and the displacements and no effect on the compress and shear stresses. The influence of different material parameters, layer height, span-depth ratio and friction coefficient on the analytical solutions is discussed.Based on the analytical solutions obtained, the stresses and displacements of the superposed beams are analyzed, and the analytical solutions of the isotropic superposed beams are compared with the solutions of material mechanics. The results show that the two kinds of the analytical solutions of the isotropic superposed beams are very close, the first kind of the analytical solutions of the orthotropic superposed beams is better than the second. After exchanging the upper and lower layers, the stresses in the two layers are basically unchanged, the cross sections of two layers are still maintained as the plane after deformation. When there is friction in the interface, the bearing capacity of the superposed beam is improved, and the stress values on the exterior sides are larger than that on the interior sides, and the neutral layers in two layers are shifted from the corresponding geometric mid-planes to the interface. When both the larger elastic modulus and the larger height are in the same layer, the bearing capacity of the superposed beams is improved. The analytical solutions of the orthotropic superposed beams can be degenerated into that of the isotropic superposed beams.The numerical analyses are carried out respectively for the isotropic and the orthotropic superposed beams by using the software ANSYS14.0 of finite element analysis and compared with the analytical solution. The results show that the analytical solutions coincide with the FEM solutions well, so the validity of the analytical solutions is verified.