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

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. This paper was recommended for publication in revised form by Associate Editor Joo Ho Choi T. S. Jang, the corresponding author of the paper, is by birth a Korean, with Naval Architecture and Ocean Engineering Ph.D degrees from Seoul National University, who worked at the department of Naval Architecture and Ocean Engineering in Pusan National University from 2003 until now. His main field of research has been the optimization theory, water wave motion and inverse problem with special focus on ocean-related fields