A biparametric perturbation method for the Föppl-von Kármán equations of bimodular thin plates

In this study, a biparametric perturbation method is proposed to solve the Föppl-von Kármán equations of bimodular thin plates subjected to a single load. First, by using two small parameters, one describes the bimodular effect and another stands for the central deflection, we expanded the unknown deflection and stress in double power series with respect to the two parameters and obtained the approximate analytical solutions under various edge conditions. Due to the diversity of selection of parameters and its combination, by using the bimodular parameter and the load as two perturbation parameters, we elucidated further the application of this method. The use of two sets of parameter schemes both can obtain satisfactory perturbation solutions; the numerical simulations also verify this idea. The results indicate that in a biparametric perturbation method, the selection and its combination of parameters may reflect the combined effects introduced by nonlinear factors. The method proposed in this study may be used for solving other mathematical equations established in some application problems.