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Boundary element analysis of contact problems using inverse techniques—linear and quadratic elements

This paper presents an inverse boundary element (BE) technique to reconstruct the boundary conditions in contact regions using photoelastic measurement data consisting of the differences of the principal stresses and their orientations at interior points. The separate individual Cartesian stress components are then obtained using the conventional ‘forward’ boundary element method (BEM). Numerical experiments show that using linear elements instead of quadratic elements can reduce the sensitivity of the inverse BEM to the errors of photoelastic measurements and gives better results. A smoothing displacement scheme is further introduced to improve the accuracy of the reconstructed tractions. When up to 5, 10 and 20 per cent random ‘noise’ was added to the simulated measurement data, the results of the inverse BE analysis still show good agreement with reference solutions. An example using real photoelastic measurements on a simple specimen is also presented and the results are found to be encouraging.