Abstract: The properties of the fundamental solution are derived in linear elastostatics. These properties are used to show that the conventional displacement and traction boundary integral equations yield non-unique displacement solutions in a traction boundary value problem. The condition for the existence of unique displacement solutions is proposed for the traction boundary value problem. The degrees of freedom of the displacement solution are removed by the condition to obtain the boundary integral equations of unique solutions for the traction boundary value problems. Numerical example is presented to demonstrate the accuracy and efficiency of the present equations.

Key words: boundary integral equation, boundary element method, elasticity