This paper presents the derivation of non-singular boundary integral equations (BIEs) of displacements in three dimensional elasticity problems. In contrast to the strongly singular and weakly singular integral representations, the numerical computation of the nearly singular integrals is eliminated because all the integrands are made finite in this formulation even if the internal point approaches the boundary. So more accurate and continuous solutions can be obtained by using the standard Gaussian quadrature not only in the domain but also near the boundary. This paper presents the derivation of weak singular boundary integral equations of stresses in three dimensional elasticity problems. This presentation is very simple and general obtaining a field solution not only near a smooth surface but also near a sharp corner or an edge.
Three test problems are analyzed in which we present a comparison of the accuracy achieved by the numerical computations based on the use of weakly singular and non-singular integral representations of displacements and one of strongly singular and weakly singular integral representations of stresses. In addition, stresses on the boundary can be evaluated by interpolation and numerical differentiation.