Numerical calculation of the elastic field in a half-space using bilinear elements

This paper considers the problem of computing the stresses inside an elastic half-space for prescribed normal and shear surface tractions. It is shown that piecewise constant loading elements result in numerical artifacts near the element boundaries. This is resolved by approximating the surface loading using bilinear elements. Three different implementations are considered, namely Dydo and Busby's approach on the basis of potential functions, a new approach on the basis of explicit formulas, and using numerical integration. The results are thoroughly cross-validated, revealing subtle issues in the earlier works. These new results are then used to establish the reliability of a practical way forward, using the piecewise constant approach, computing values at element centers only.