NONLINEAR DYNAMICS OF SIMPLE SHELL-MODEL WITH CHAOTIC SNAPPING BEHAVIOR

A simple spring-mass numerical model (MSHELL), is developed as a tool to find appropriate integration time steps for nonlinear finite-element analysis. MSHELL possesses many features of nonlinearly deforming deep shells and, by matching some physical parameters of the MSHELL system and a nonlinear finite-element model (DSHELL), their dynamic behavior is both qualitatively and quantitatively similar. MSHELL is used to develop time-step criteria fpr both pre- and postsnapping behavior of a transversely pointloaded cylindrical shell. The criteria are then applied in a multiple-time-step method to DSHELL. The results indicate the simple model's correlation with the finite-element model and potential for saving computer time by changing the integration time step during a finite-element analysis based on MSHELL's behavior. Chaotic motion, characterized by one or more positive Lyapunov exponents, is seen in the simple model and likely explains unpredictable postcollapse results in the DSHELL finite-element code.