A non-hypersingular boundary integral formulation for displacement gradients in linear elasticity

Based on boundary displacement and traction, a non-hypersingular boundary integral formulation is developed for the displacement gradient. At an arbitrary boundary point where the displacement field at least satisfies a Hölder condition (u_k ε C^1,γ with γ > 0), the displacement gradient can be calculated by the Cauchy Principal Value (CPV) integration. The hypersingularity involved in conventional formulation is circumvented by applying rigid body translation. The numerical implementation of the present formulation is illustrated, and both direct and indirect approaches are discussed. For two-dimensional problems, the coefficients involved in the direct approach are analytically derived. The stress formulation is also discussed. Finally, numerical examples are presented to validate the present formulation.