A NEW APPROACH FOR IDENTIFYING THE BENDING LOADS ON BEAM USING THE DISCRETE INTEGRAL METHOD Hiroyuki Kisu , Guiming Rong and Yoshihiro Kondo Faculty of Engineering, Nagasaki University, Bunkyo-machi 1-14, Nagasaki 852, Japan Graduate School of Marine Science and Engineering, Nagasaki University ABSTRACT Analysis of inverse problems has already been performed in various fields. In many cases, assumptions for the solution is needed. It seems that the problems which need any assumptions cause a contradiction in the analysis. On the other hand, we have developed the discrete integral method(DIM) utilizing the delta function. We have noticed that the DIM is one of the excellent schemes to solve the inverse problem since it can solve it without any assumptions. In this paper, we attempt to apply the DIM to one-dimensional inverse problems. Namely, we developed a scheme for identifying the external load distribution on a homogeneous beam without any assumption for the solution. Through several examples, it is proved that the present scheme gives accurate and natural solutions. KEYWORDS Boundary element method, Discrete integral method, Inverse problems, Bending problems of beam INTRODUCTION In the analysis of Inverse Problem[1,2], many points of issue have been left yet even if problems with ill-conditions are excluded. One of them is concerning presumption. This means that, it is necessary to give assumption information such as the shape, the number, its size or position and so on, of the object to be treated, as supplementary information for identification. It is difficult to solve it as an inverse problem if several assumptions concerning priori information are not defined, for the subject to be estimated is a unknown existence. In addition, the unnatural equations must be used when the number of parameters is different from that of simultaneous equations which works as a deciding condition. These cause the difficulty to establish a general scheme in the analysis of inverse problems. For these reasons, it is important to establish a scheme for inverse problems without any assumptions of the solution. In this study, the first time, the discrete integral method utilizing the delta function is developed and we try to apply this method as one of schemes to the analysis of inverse problem by boundary element method (BEM). It is shown that the identification is performed naturally without any assumptions of the solution by
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