Formulation of static and dynamic layered beam systems with an inverse problem.

Abstract

Mathematical models are developed to examine the interfaces of horizontally-layered beam systems. The application examined is that of concrete road overlays. We are particularly interested in how the normal displacement of the beams is affected by the shearing interface coefficient, KS. We ignore any effect due to friction. Both the static and dynamic models developed in this paper allow for cavitation between the two beams. This in effect corrects the problem of one beam penetrating the other and allows us to try to predict where the two beams may actually separate. Also, with the addition of the time-dependent model, we can add a moving mass or rolling load. The static two-beam model gives results which were validated by laboratory data. We show that a unique solution exists and that this solution continuously depends on the parameter KS. We also formulate the problem for multilayered systems. For the dynamic model, we show the existence of a unique solution to the weak form of the problem. We then consider a numerical example of an inverse problem in which we attempt to recover K S using data generated from the forward problem.