A nonlinear model of thick shells for large-amplitude vibrations

Nonlinear shell modeling is always accompanied by simplifying assumptions on some computational parameters. In the latest nonlinear model based on eight parameters, that considers the displacement field as third-order polynomials in all three directions of curvilinear system, rotational inertia and shear deformations are also included; however, nonlinear terms are eliminated from some dependent variables, in addition, curvature and torsion variations of the shell are also assumed linear. In this study, not only all the dependent variables were considered as nonlinear in a different approach, but curvatures and torsion nonlinearities also retained, and a complete and accurate model for thick shells of any shape was presented. The equations of motion of the system have been derived on the basis of Lagrange equations, and cylindrical shells under static and dynamic loads have been studied. In the case of static loading, it was seen, with increasing the shell thickness, the effects of nonlinear curvature and torsion were limited, but have a significant impact on post-buckling behavior of the shell, where noticeable large deformations have occurred. However, their effects in static loading were less than the dynamic case, especially the aftermath of the buckling. It was also observed in dynamic loading, while the nonlinearities of curvature and torsion raised the system frequency content, it also intensifies the vibration amplitude and changes the response style to the dynamic excitation.

Automated summary

Nonlinear shell modeling involves simplifying assumptions on computational parameters. The latest model considers displacement field as third-order polynomials, including rotational inertia and shear deformations, while eliminating nonlinear terms from some dependent variables. Nonlinearities of curvature and torsion were retained in this study, impacting the post-buckling behavior and dynamic response of the shell.