MVM Energy Method for Buckling Analysis of Tapered Plates

Tapered plates are being increasingly used in modern engineering structures. The increasing use is due to the distributed flexural stiffness that helps reduce the weight of structural elements and improve the utilization of the material. The flexural stiffness, vibrational, and buckling capacities of these plates may be significantly increased by appropriate tapering. On the other hand, provision of openings in perforated plates which provide access for inspection, services, and maintenance, can greatly enhance the applicability of these members in many structures such as platforms, naval and aeronautical structures. Beside these advantages, openings result in a reduction of the buckling capacity, which should be taken into account. n this paper a new exact solution procedure using energy method based on modified vibrational mode shapes is formulated for the buckling analysis of simply supported rectangular plates of abruptly varying stiffness subjected to uniform edge stresses. It is shown that the vibrational mode shapes of a tapered plate is in fact a linear combination of various mode shapes of intact plates. This phenomenon is used to estimate the vibrational mode shapes of taper plates, and is then incorporated to evaluate the buckling loads.