The nonlocal solution of the elastic half-plane loaded at the origin by shear force

In this paper, the nonlocal continuum theory is applied to the problem of elastic half plane loaded at the origin by a force P directed along x axis. The solution of this problem in the frame of classical elasticity can be found in every reference book of elasticity. First constitutive equations of nonlocal theory is given. The nonlocal stress field is determined. According to the classical elasticity solution of this problem, stresses become infinite at the application point. That is, classical elasticity solution is not valid in the neigbourhood of origin. To remedy this situation nonlocal continuum theory is used. The results are compared with the classical elasticity solution. Interestingly enough none of the classical singularities exist in the nonlocal solution.