Bounds on Large Dynamic Deformations of Structures

Response of rigid-plastic structures to a certain class of dynamic loadings is investigated taking into account changes in geometry and interactions between bending moments and membrane forces. Starting from the usual assumption of the theory of moderately large deflection of shells and introducing a suitably modified principle of virtual velocities, bounds on permanent deflections of structures are established. In the limiting case of small deflections the present solution reduces to the earlier result due to Martin. The general procedure is explained on the example of simply supported circular plate loaded impulsively. The obtained bound on central deflection is compared with exact solution of the same problem and with Florence experimental data on aluminum plates. It is shown that considerable improvement is achieved relative to the simple bending solution. The present bounding curve closely follows the trend of experimental points over the whole range of applied impulse.