Elastic response of a free half-space to random force excitations applied on the boundary

A response of an elastic half-space to random forces applied normally to the free boundary is studied. This paper is the second part of the study we presented in [I.A. Shalimova, K.K. Sabelfeld, The response of an elastic three-dimensional half-space to random correlated displacement perturbations on the boundary, Physica A 389 (21) (2010) 4436–4449] where the case of random displacements on the boundary was considered. We analyze the white noise excitations in detail, and derive explicitly the mean of the elastic energy, the strain and displacement correlation tensors. Simulation algorithms are constructed both for displacement and strain random fields, which enables us to calculate any desired statistical characteristics. ► A response of a free elastic half-space under normal boundary random forces is analyzed. ► We derive explicit formulae for the correlation tensor in the case of white noise forces. ► The formulae obtained make it possible to analyze the fields from general point defects. ► The mean elastic energy is obtained in the form of an explicit and simple expression.