Static analysis and buckling of viscoelastic plates by a fully discretized nonlinear finite strip method using bubble functions

A semi analytical finite strip method is developed for the analysis of viscoelastic plates with different end conditions using bubble functions. Each plate may be subjected to different types of out-of-plane and in-plane loading. The displacement functions of plate are evaluated using a continuous harmonic function series that satisfies the boundary conditions in the longitudinal direction and a piecewise interpolation polynomial in the transverse direction. The mechanical properties of the material are considered to be linear viscoelastic by expressing the relaxation modules in terms of Prony series. The fully discretized finite strip equations are developed using a two point recurrence formulation. Time history of maximum deflection of plates with different end conditions is calculated in the present study. In addition, the effect of unloading on plates is evaluated. Moreover, a nonlinear approach is used to calculate the critical load of plates subjected to in-plane compressive loads.