Authors: K Tolstikhin
Publish Date: 2016/05/26
Volume: 103, Issue: 1, Pages: 87-95
Abstract
The problem of differentiating nonsmooth functions of specimen displacements which are measured during the material removal is discussed This problem arises when employing the layer removal method namely a method of rings and strips for residual stress depth profiling It is shown that this problem is illposed and special solution methods are required in order to obtain a stable solution The stability of the solution affects to a high extent the resulting accuracy of the residual stress evaluation in the investigated material The presented study discusses a numerical approach to solving such illposed problems The proposed approach which is based on the Tikhonov regularization and a regularized finite difference method provides a stable approximate solution including its pointwise error estimation The advantage of this approach is that it does not require any knowledge about the unknown exact solution the pointwise error estimation of the measured data is the only prior information that must be available In addition this approach provides a convergence of the approximate solution to the unknown exact one when the perturbation of the initial data approaches zeroThis research was supported by the Government of Russian Federation the Ministry of Education and Science Project No 201221803120 The author is deeply grateful to his late colleague Prof Zamashchikov for the insightful discussions and the valuable research assistance
Keywords: