Elastic–Plastic Deformation Analysis of Cantilever Beams with Tension–Compression Asymmetry of Materials

In the elastic-plastic analysis of structures, the deformation problem of cantilever beams is a classical problem, in which it is usually assumed that the material constituting the beam has an identical elastic modulus and identical yield strength when it is tensioned and compressed. These characteristics are manifested graphically as the symmetry of tension and compression. In this work, we will give up the general assumption and consider that the material has the property of tension-compression asymmetry, that is, the material presents different moduli in tension and compression and different yield strengths in tension and compression. First, the elastic-plastic response of the cantilever beam with a concentrated force acting at the fixed end in the loading stage is theoretically analyzed. When the plastic hinge appears at the fixed end, the maximum deflection at the free end is derived, and in the unloading stage the residual deflection at the free end is also given. At the same time, the theoretical solution obtained is validated by the numerical simulation. The results indicate that when considering the tension-compression asymmetry of materials, the plastic zone length from the fixed end no longer keeps the classical value of 1/3 and will become bigger; the tension-compression asymmetry will enlarge the displacement during the elastic-plastic response; and the ultimate deflection in loading and the residual deflection in unloading are both greater than the counterparts in the classical problem. The research results provide a theoretical reference for the fine analysis and optimal design of cantilever beams.