An Elasto-Plastic Stress Analysis in a Polymer–Matrix Composite Beam Supported from Two Ends under Transverse Linearly Distributed Load by Use of Anisotropic Elasticity Theory

An analytical elasto-plastic stress analysis is carried out in a low-density polyethylenethermoplastic beam supported from two ends under transverse linearly distributed load reinforced by Cr–Ni steel fibers analytically. The material is assumed to be perfectly plastic for the elasto-plastic solution. The intensity of the uniform force is chosen at a small value; therefore, the normal stress component y is neglected in the elastic–plastic solution. The expansion of the plastic region and the residual stress component of σ_x and τ_xy are determined for 0, 30, 45, 60, and 90 orientation angles. The yielding begins at the upper and lower surfaces of the beam at the same distances from the ends. The intensity of residual stress component of x is maximum at the upper and lower surfaces but residual stress component of τ_xy is maximum on the x axis of the beam. The strength of the beam is increased by residual stresses.