Numerical experiments on determination of spatially concentrated time-varying loads on a beam: an iterative regularization method

Abstract

This paper treats a solution for the ill-posed (inverse) load determination problem for a time-varying load on a beam. The ill-posed nature of the problem causes numerical instability. Conventional numerical approach for solutions results in arbitrarily large errors in solution. The Tikhonov regularization method, which is a non-iterative stabilization technique, has been widely adopted for overcoming the ill-posed nature (or numerical instability). However, in this paper, we introduce an “iterative” regularization method, specifically, the iterated Tikhonov regularization method. The iterated method is applied to the present load determination problem. The result of the iterative method is compared with that of the (non-iterative) Tikhonov regularization. The rate of convergence for the introduced iterative method turned out to be very fast. The accuracy and applicability of the introduced method are examined through a numerical experiment.