A regularization method for calculating engineering loads from strain data

摘要

A preliminary study of a new method of determining interface pressures in contact zones between hard and soft elastic bodies from measurements of strain away from the contact zone is carried out using a single beam with a known load on its topside and strain gauges spaced out along its underside. The beam is such that it can be modelled by simple beam theory. To reconstruct the load from the strain data a regularization scheme of projection type based on the non-negativeness of the pressure distribution is developed. The distribution is represented as a series of basis functions, here either Bernstein polynomials or quadratic B-splines, the coefficients in the series being determined by solving a constrained optimization problem. This method of reconstruction is applied to known theoretically simulated loads with random noise added and to experimental loads, and ways of determining good values of the regularization parameter, the number of basis functions, given. The reconstructions obtained are very satisfactory and give confidence in the application of the method to unknown loads.