We have developed a non-iterative algorithm for determining unknown deformations and tractions on surfaces of arbitrarily shaped solids where these quantities cannot be measured or evaluated. For this inverse boundary value technique to work, both deformations and tractions must be available and applied simultaneously on at least a part of the object's surface called an over-specified boundary. Our method is non-iterative only because it utilizes the boundary element method (BEM) to calculate deformations and tractions on surfaces where they are unavailable and simultaneously computes the stress and deformation field within the entire object. Inversely computed displacement and stress fields within simple solids and on their boundaries were in excellent agreement with the BEM analysis results and analytic solutions. Our algorithm is highly flexible in treating complex geometries and mixed elastostatics boundary conditions. The accuracy and reliability of this technique deteriorates when the known surface conditions are only slightly over-specified and far from the inaccessible surfaces.
