Boussinesq–Flamant problem in gradient elasticity with surface energy

The strain gradient elasticity theory with surface energy is applied to Boussinesq–Flamant problem. The solution for the vertical displacements at the surface of half space due to the surface normal line load is presented. The theory includes both volumetric and surface energy terms. Boussinesq–Flamant problem in the strain gradient elasticity is solved by means of Fourier transform. The results obtained show that the vertical displacements of half space in the gradient elasticity are some different from that in the classical elasticity and the effects of the strain gradient parameters (material characteristic lengths) on the vertical displacements do exist.