Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments

Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for a simply supported stiff thin film resting on a two-parameter elastic foundation in thermal environments. The stiff thin film is modeled as a nonlocal orthotropic plate which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of the substrate are assumed to be temperature-dependent. The governing equation that includes plate-foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies, but increases the nonlinear to linear frequency ratios of the thin film slightly. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of the thin film resting on an elastic foundation.