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

Abstract

The present investigation deals with the nonlinear analysis of the dynamic buckling response and global stability aspects of two 3-DOF spring-mass, initially imperfect dissipative simplified structural models under step loading, simulating elastic shell panels of revolution and in particular a spherical cap and a conical panel. It is found that snapping, which is the main characteristic of the actual continuous structures, is successfully captured by the proposed simulations, which following a straightforward nonlinear approach are found to exhibit dynamic snap-through buckling, associated with a point attractor response in the large, implying global stability. Furthermore, the presence of physically not accepted complementary equilibrium configurations does not affect the long term response of the autonomous systems dealt with, but only complicates the motion and elongates the time before the final steady state. Finally, the criterion of zero total potential energy yields excellent lower bounds of the exact dynamic buckling loads, very important for structural design purposes.