A non-hypersingular boundary integral formulation for displacement gradients in linear elasticity (Q1271635)

Based on boundary displacement and traction, we derive a non-hypersingular boundary integral formulation for the displacement gradient. At an arbitrary boundary point where the displacement field satisfies at least a Hölder condition \((u_k\in C^{1,\gamma}\) with \(\gamma>0)\), the displacement gradient can be calculated by the Cauchy principal value integration. The hypersingularity involved in conventional formulation can be circumvented by applying rigid body translation. A numerical implementation illustrates the present formulation, and both direct and indirect approaches are discussed.