Large deflection analysis of rectangular plates on two-parameter elastic foundation by the boundary strip method

A method is proposed for calculating the large deflection of a rectangular plate on an elastic foundation by the boundary integral equation method. The elastic foundation is assumed to be of the Pasternak type. The large deflection is formulated based on the nonlinear Berger equation. In the analysis, the governing nonlinear partial differential equation for a plate is transformed into an ordinary nonlinear differential equation using the Kantrovich method. The resultant fourth-order nonlinear differential equation was analyzed by the boundary element method. The nonlinear boundary integral equation is solved by using an iteration scheme. A fundamental solution required in the formulation is derived by solving the singular differential equation. It is found that the numerical results obtained by the present method agree well with the analytical solutions. To show the usefulness of the method, several numerical results based on the present formulation are given for various types of boundary and loading conditions.