Geometrically Nonlinear Transient Response of Laminated Plates with Flexible Supports

Abstract

Laminated plates are loading-bearing components that are generally connected to flexible pads and exhibit complicated mechanical responses. To investigate the geometrically nonlinear transient responses of a laminated plate with flexible pad supports, a varied constraint reaction model and a systematic numerical procedure are presented in this paper. The flexible pad supports of the plate were treated as viscoelastic boundary conditions, wherein the strip-type pad per unit length was modeled as a cantilever beam. The nonlinear Kelvin–Voigt model was developed to simulate the nonlinear viscoelastic behaviors of the flexible pads. The dynamically varied constraint reactions generated by the viscoelastic supports, which depend upon the displacement and velocity of the nodes along the plate edge, were determined by the deflection and slope equations of the beam theory used, and they were applied on the plate edges by using the nonlinear load functions. Thus, the dynamical responses of the laminated plate with viscoelastic supports were obtained. Numerical results show that the present method can effectively treat the geometrically nonlinear transient response of the laminated plate with viscoelastic supports, and it is essential to consider the effects of non-ideal boundary conditions in the nonlinear transient analysis.