Investigation of the generalized solution behavior for the transverse deflection of a rigid-plastic clamped plate: Eccentric and multiple punches loading

Abstract

For most of the studies concerning about the transverse deflection of plates subjected to the loading of a rigid punch, the sections of the punch and the plate are usually circular and concentric. However, eccentric loading conditions in which the punch and the plate may not be circular and concentric have seldom been discussed. This paper firstly studied the solution behavior for a rigid-plastic clamped plate under quasi-static eccentric loading conditions based on the theory of rotation-rate continuity and the method of fundamental solutions (MFS). For eccentric loading, four types of loading conditions have been applied: circular punch vs circular plate (CC), circular punch vs elliptical plate (C-E), elliptical punch vs circular plate (E-C) and elliptical punch vs elliptical plate (E-E). The load position of the punch is also arbitrary with respect to the plate. Contour lines of transverse deflection, principal stress and strain and punching force-punch displacement curves have been obtained for different loading conditions. It has been proved that the circuit integral of the product of transverse deflection gradient and contour line's outer normal is constant for any contour line, leading to a linear relationship between the punching force and deflection of the punch. It turns out that the ratio of punch section area to plate section area and the deviation distance of the punch center from the plate center will both influence the value of the circuit integral term, which is correlated with the punching force, as they increase the punching force will also increase if the punch displacement is fixed, and vice versa. Finally, accounting for the merits of MFS in solving the Laplace equation, the solution procedure can be extended to multiple punches loading conditions. Results have revealed that rotation-rate continuity still prevails in rigid-plastic solids in this case. Finite element analysis has been conducted to show that its results agree with the analytical results at a satisfactory level.