Nonlinear stability of simplified structural models simulating elastic shell panels of revolution under step loading

The present investigation deals with the nonlinear analysis of the dynamic buckling response and global stability aspects of two 3-DOF spring-mass, in itially imperfect dissipative simplified structural models under step loadi ng, simulating elastic shell panels of revolution and in particular a spher ical cap and a conical panel. It is found that snapping, which is the main characteristic of the actual continuous structures, is successfully capture d by the proposed simulations, which following a straightforward nonlinear approach are found to exhibit dynamic snap-through buckling, associated wit h a point attractor response in the large, implying global stability. Furth ermore, the presence of physically not accepted complementary equilibrium c onfigurations does not affect the long term response of the autonomous syst ems dealt with, but only complicates the motion and elongates the time befo re the final steady state. Finally, the criterion of zero total potential e nergy yields excellent lower bounds of the exact dynamic buckling loads, ve ry important for structural design purposes. (C) 2001 Elsevier Science Ltd. All rights reserved.