Inverse determination of the loading source of the infinite beam on elastic foundatlon

Abstract

The primary aim of the paper is to identify the loading source of infinite beams on an elastic foundation from given information of vertical deflection of infinite beams. An integral equation is obtained for the relationship between loading distribution and vertical deflection. It is shown that the inverse identification of a loading source is one-to-one but ill-posed. Because of ill-posedness, the usual numerical schemes produce arbitrarily large errors. A method for the solution is proposed by using Tikhonov's regularization. L-curve criterion is introduced for the determination of optimal regularization parameter. Numerical experiments show that the present methodology is accurate and robust in the inverse determination of loading source.